In Euclidean geometry, which of the following is the standard way to name a plane?

Using three non-collinear points on the plane

Using the name of a line contained within the plane

Using any two points located on the plane

Using a single capitalized letter representing a point

Which of the following is true regarding the naming conventions of the angle formed by rays \vec{BA} and \vec{BC} ?

The angle can be named \angle ABC or \angle CBA .

The angle can only be named \angle B if it is the only angle at that vertex.

The angle can be named \angle ACB if point C is higher than point A.

The angle must be named \angle BAC because A comes first alphabetically.

Which of the following is the most appropriate way to name the point where two lines intersect?

A single capital letter, such as P

A set of two capital letters, such as PQ

A capital letter with a line symbol, such as \overleftrightarrow{P}

Point, line, plane, ray, line segment, angle

Point Line Plane etc....

Tobruk, a small town on the Libyan coast, was central to much of the fighting that took place in the Western Desert during the Second World War. It had originally been developed by the Italians during their colonisation of eastern Libya during the early decades of the 20th century. With a sheltered deep water harbour it became a key naval outpost. It was fortified during the 1930s with both coastal defence batteries and a 50 kilometre-long perimeter of reinforced concrete platoon posts, and other supporting infrastructure such as gun positions, headquarters bunkers, underground supply dumps, and observation towers. When British and Commonwealth forces advanced out of Egypt and into Libya in January 1941, Tobruk was their second objective. The Italian defence perimeter was attacked by the 6th Australian Division on the morning of 22 January and the town fell the next morning. The operation resulted in approximately 27,000 Italian prisoners and the capture of over 200 artillery pieces, but cost 49 Australian lives. The 6th Division's advance pressed on beyond Tobruk and eventually they were withdrawn from Libya to be deployed to Greece.The 9th Australian Division was moved in to Libya in February 1941 to garrison the territory captured by the 6th. By this time, however, German troops had arrived in Libya to reinforce their Italian allies and they launched an offensive that the British Commonwealth forces were ill-disposed to hold back. A retreat towards Egypt commenced. The 9th Division was ordered to fall back upon Tobruk, hold it in order deny its port facilities to the Germans, and delay their advance so as to provide time for defences on the Egyptian frontier to be prepared. Tobruk and the 9th Division were subsequently encircled, beginning what became known as "the siege of Tobruk". Reinforced by the 18th Brigade of the 7th Australian Division and other British and Commonwealth troops, and resupplied by the sea, the 9th Division held Tobruk from April to September 1941. During this period it repelled two major German attacks. In September and October the 9th Division, its condition steadily declining, was relieved by the British 70th Division, which continued to defend Tobruk until the siege was finally lifted by Operation Crusader in December. The defence of Tobruk resulted in 749 Australian deaths, and another 604 became prisoners of war. Tobruk was the scene of further heavy fighting in June 1942 when the fortunes of war again saw a British Commonwealth force seeking to deny the port to the enemy. The Axis forces, however, were in no mood for another siege and launched a massive attack to capture it on 20 June. It remained in their hands until their final retreat from Libya in November 1942.John Hurst Edmondson (1914-1941), soldier, was born on 8 October 1914 at Wagga Wagga, New South Wales, only child of native-born parents Joseph William Edmondson, farmer, and his wife Maude Elizabeth, née Hurst. The family moved to a farm near Liverpool when Jack was a child. Educated at Hurlstone Agricultural High School, he worked with his father and became a champion rifle-shooter. He was a council-member of the Liverpool Agricultural Society and acted as a steward at its shows. Having served (from March 1939) in the 4th Battalion, Militia, he enlisted in the Australian Imperial Force on 20 May 1940 and was posted to the 2nd/17th Battalion. Later that month he was promoted acting corporal (substantive in November). Well built and about 5 ft 9 ins (175 cm) tall, Edmondson settled easily into army life and was known as a quiet but efficient soldier. His battalion embarked for the Middle East in October and trained in Palestine. In March 1941 the 2nd/17th moved with other components of the 9th Division to Libya and reached Marsa Brega before an Axis counter-attack forced them to retreat to Tobruk. The siege of the fortress began on 11 April. Two days later the Germans probed the perimeter, targeting a section of the line west of the El Adem Road near Post R33. This strong-point was garrisoned by the 2nd/17th's No.16 Platoon in which Edmondson was a section leader. The enemy intended to clear the post as a bridgehead for an armoured assault on Tobruk.Under cover of darkness thirty Germans infiltrated the barbed wire defences, bringing machine-guns, mortars and two light field-guns. Lieutenant Austin Mackell, commanding No.16 Platoon, led Edmondson's five-man section in an attempt to repel the intruders. Armed with rifles, fixed bayonets and grenades, the party of seven tried to outflank the Germans, but were spotted by the enemy who turned their machine-guns on them. Unknown to his mates, Edmondson was severely wounded in the neck and stomach. Covering fire from R33 ceased at the pre-arranged time of 11.45 p.m. and Mackell ordered his men to charge. Despite his wounds, Edmondson accounted for several enemy soldiers and saved Mackell's life. When the remaining Germans fled, the Australians returned to their lines. Although Edmondson was treated for his wounds, he died before dawn on 14 April 1941. The Germans' armoured attack that morning was thwarted, partly due to the earlier disruption of their plans. Edmondson was buried in Tobruk war cemetery. He had not married. His Victoria Cross, gazetted on 4 July, was the first awarded to a member of Australia's armed forces in World War II. In April 1960 Mrs Edmondson gave her son's medals to the Australian War Memorial, Canberra, where they are displayed alongside his portrait (1958) by Joshua Smith. At Liverpool a public clock commemorates Edmondson, as do the clubrooms used by the sub-branch of the Returned Services League of Australia.Perhaps my nerves will be more under control when I am by myself. There were no entries in the diary until Friday April 18 when she wrote: Fighting terrific in Greece and North Africa…. I dread the casualty list also the heaviest air raid over London to date. Account …. of heavy fighting and much use of bayonet at Tobruk. Also gives an account of a charge in which a Lieutenant and a Corporal took prominent parts on Easter Sunday night. Of course, no names. When I read it …. I was sure the Corporal was Jack…. It said no casualties but …. I know … that all is not well with Jack. ….. (and) Stuffy ….has not come home yet. On Wednesday April 23 she received a letter from Jack dated March 30 and for the first time he said the conditions were bad. The food short, water one bottle for 48 hours. It worried me terribly so I posted a parcel (of) milk tablets, chocolate milk, biscuits (and) cigarettes.Tuesday April 15 I was feeling afraid of something while I was working and packing the cake (and) had a couple of brandys to (keep going).April 26 Received the following telegram in the mail, the bus man brought it in. “It is with deep regret that I have to inform you that Corporal John Hurst Edmondson was killed in action on the 14th April and desire to convey the profound sympathy of the Ministry for the Army and the Military Board.”Her final entry

A Brief History of Washington’s Crossing of the Delaware River, Christmas Night 1776... In the fall of 1776, General George Washington and his army had suffered a series of defeats at the hands of the British Army. The Continental Army had lost every battle with the British in the New York campaign: Long Island, Manhattan, Brooklyn Heights, Harlem and White Plains and had surrendered Fort Washington and Fort Lee. At Fort Lee, the army barely escaped and was forced to leave behind its store of provisions, ammunition, and many of its weapons. A sense of defeat had settled around Washington as he was forced to retreat across New Jersey in November and finally to Pennsylvania on December 8, 1776. The British, at least, considered the war over. By December 11th, the only reason the British had not taken Philadelphia, the seat of the Continental Congress, was that Washington had ordered every boat in the Delaware River on the New Jersey side to be brought to the Pennsylvania side, thus denying the British army transportation. Washington knew that the British would be capable of resuming an offensive by crossing the Delaware once it iced over. As the harsh winter set in, the morale of the American troops was at an all-time low. The soldiers were forced to deal with a lack of both food and warm clothing, while Washington watched his army shrink because of desertions and expiring enlistments. Now, more than ever, a victory was desperately needed. Washington devised a courageous plan to take the offensive and cross the Delaware River on Christmas night and attack the Hessian garrison at Trenton, New Jersey, nine miles south of his encampment near McConkey's Ferry. The original plan called for three divisions to cross the Delaware under the cover of darkness. Lt. Col. John Cadwalader's division was to cross at Bristol and engage the southern most contingent of British forces — Hessian troops under the command of Colonel von Donop. General James Ewing's division was to cross at Trenton Ferry and take a position south of Assunpink Creek below Trenton and hold the bridge over that stream. Washington's division was to cross at McConkey's Ferry and then divide into two corps under General Nathanael Greene and General John Sullivan. Their point of attack was Trenton and the Hessian troops quartered there under the command of Colonel Johann Gottlieb Rall. The boats to be used for the crossing were gathered earlier in the month in compliance with General Washington's orders, primarily as a defensive measure. Various types of boats had been collected, most notably the large Durham boats used to carry pig iron down the Delaware to the Philadelphia markets. There were a number of problems in moving a large number of men, cannons, and supplies in an age when overland transportation was by foot and animal power. The roads were rutted and winding. There were no bridges over major rivers because the technology did not exist to span great distances. A river like the Delaware was crossed by ferry, sometimes out of service because of ice floes or floods, and certainly not designed to carry masses of men and equipment across quickly. A river could be a formidable natural barrier to an army on the move. Washington had several logistical concerns for the crossing. In addition to the troops were the cannon; each of which required at least two horses to pull it. The heavier twelve pounders, and probably the eight pounders, had four horses. There would have been between four and six ammunitions wagons. Officers of the rank of colonel or higher may have had horses. In sum, Washington had to move 2,400 men, eighteen cannons, at least four ammunition wagons and fifty to seventy-five horses across the Delaware River the night of December 25, 1776. Fully expecting to be supported by Cadwalader's and Ewing's divisions south of Trenton, Washington assembled his own troops near McKonkey's Ferry in preparation for the crossing. By 6:00 pm, 2,400 men had begun crossing the ice-chocked river. There was an abrupt change in the weather, forcing the men to fight their way through sleet and a blinding snowstorm. The river was flooded with sheets of ice moving at eleven or twelve miles per hour. These obstacles proved to be too much for the two supporting divisions led by Generals Cadwalader and Ewing, who did not cross at their assigned points along the river. It was Washington's pure force of will and determination that led to his troops' successful crossing of the river. Increasing Washington's odds were the sailors of Marblehead, Massachusetts. This group of hardened seamen, led by Col. John Glover, were used to the Nor'easters of New England. Sheer determination and muscles conditioned to the demands of rowing under the weather conditions now facing the Continental army enabled the Marbleheaders to row back and forth across the Delaware countless times. During the time of the Revolution, American soldiers marched single file along the margins of the roads. They were only assembled into a battle line (three deep) when they reached the battlefield. The battle plan had Washington's army marching in two divisions... General Greene's and General Sullivan's. They made a night march in two columns on separate roads, a very tricky operation that was prone to failure since the columns needed to arrive at the battlefield at the same time to carry out the surprise attack planned by Washington. The American army carried out the march flawlessly. Against all odds, Washington and his men successfully completed the crossing and marched to Trenton on the morning of December 26th and, in the resulting battle, achieved a resounding victory over the Hessians. By moving ahead with his bold and daring plan, General Washington reignited the cause of freedom and gave new life to the American Revolution.

Land warfare is a complex domain that involves the application of military power on the ground to achieve political and strategic objectives. Modern military doctrine, such as that used by the U.S. Army and the Indian Army, categorizes these elements into Combat Power and the Principles of War. 1. The 8 Elements of Combat Power Combat power is the total means of destructive, constructive, and information capabilities that a military unit can apply. It is typically broken down into eight key elements: ElementDescriptionLeadershipThe "multiplier" of all other elements. It provides purpose, direction, and motivation to soldiers.InformationEnables commanders to make informed decisions and creates opportunities to achieve results.Mission CommandThe system used to integrate the other elements. It focuses on decentralized execution based on the commander's intent.Movement & ManeuverThe movement of forces to gain a positional advantage over the enemy to deliver lethal or non-lethal effects.IntelligenceThe understanding of the enemy, terrain, weather, and civil considerations.FiresThe use of weapon systems (artillery, mortars, air support) to create specific lethal or non-lethal effects.SustainmentThe logistics required to maintain operations, including ammunition, fuel, food, and medical support.ProtectionThe preservation of the force so that the commander can apply maximum combat power.2. The Principles of War These are the enduring "rules of thumb" that guide how land forces are employed strategically and tactically: Objective: Direct every operation toward a clearly defined and attainable goal. Offensive: Seize, retain, and exploit the initiative. You cannot win by defending alone. Mass: Concentrate the effects of combat power at the most advantageous place and time. Economy of Force: Allocate the minimum essential combat power to secondary efforts so you can "mass" elsewhere. Maneuver: Place the enemy in a position of disadvantage through flexible movement. Unity of Command: Ensure all forces operate under a single responsible commander toward a common objective. Security: Prevent the enemy from gaining an unexpected advantage. Surprise: Strike the enemy at a time, place, or in a manner for which they are unprepared. Simplicity: Prepare clear, uncomplicated plans to minimize confusion in the "fog of war." 3. The Modern Legal Framework Land warfare is also governed by the Law of Land Warfare (International Humanitarian Law), which rests on four pillars: Military Necessity: Actions must be necessary to achieve a legitimate military goal. Distinction: Forces must distinguish between combatants and non-combatants (civilians). Proportionality: The anticipated harm to civilians must not be excessive in relation to the concrete military advantage gained. Unnecessary Suffering: Weapons and methods must not cause gratuitous or superfluous injury. Note: Contemporary land warfare is increasingly "Multi-Domain," meaning land forces must now integrate with cyber, space, and electronic warfare to be effective. , While land warfare uses many tools, the two primary "philosophies" of how to win a war are Attrition and Maneuver. Most modern conflicts are a spectrum of both, but understanding the pure form of each helps explain military strategy. 1. Attrition Warfare: The "Sledgehammer" Attrition warfare is a strategy where one side attempts to win by wearing down the enemy to the point of collapse through continuous losses in personnel, equipment, and supplies. Core Logic: "I have more than you." It assumes that if you can destroy the enemy’s resources faster than they can replace them, you will eventually win. Focus: Firepower and mass. Success is measured by "body counts," equipment destroyed, and the steady seizing of terrain. Command Style: Usually centralized and methodical. It requires strict synchronization of massive resources (artillery, logistics, manpower). Historical Example: The Battle of Verdun (WWI). German Chief of Staff Erich von Falkenhayn famously stated his goal was to "bleed France white" by forcing them to defend a position they could not afford to lose, regardless of the cost in lives. 2. Maneuver Warfare: The "Scalpel" Maneuver warfare seeks to shatter the enemy’s moral and physical cohesion—their ability to act as a unified force—rather than simply destroying every soldier. Core Logic: "I am faster and more unpredictable than you." It aims to create a state of chaos where the enemy's leadership can no longer make effective decisions. Focus: Speed, surprise, and dislocation (forcing the enemy to be in the wrong place at the wrong time). The OODA Loop: Developed by Col. John Boyd, this is the heart of maneuver theory. It stands for Observe, Orient, Decide, Act. The goal is to cycle through these steps faster than the enemy, essentially "getting inside" their decision-making process until they collapse from confusion. Historical Example: The 1940 Invasion of France (Blitzkrieg). Instead of fighting a line-by-line battle of attrition, German forces used speed and concentrated armor to bypass strongpoints, cut communication lines, and cause a total systemic collapse of the French military in weeks. 3. Key Differences at a Glance FeatureAttrition WarfareManeuver WarfareObjectivePhysical destruction of the enemy army.Functional/Psychological collapse of the enemy.TargetThe enemy's strength (mass).The enemy's weakness (vulnerability).Primary ToolMassed Firepower.Movement and Tempo.Command"Command Push" (Top-down, rigid)."Recon Pull" (Decentralized, flexible).Success MetricExchange ratios (Kill counts).Disruption and loss of enemy control.4. The Modern Synthesis: "Schwerpunkt" In practice, no army is purely "maneuver" or "attrition." To maneuver successfully, you often need a period of attrition to punch a hole in the enemy's line. A critical concept here is the Schwerpunkt (Center of Gravity/Focus of Effort). A commander identifies the single most important place to strike and concentrates all available "elements of power" there. While the rest of the front might look like attrition, the Schwerpunkt is where the maneuver happens to achieve a breakthrough. Modern Reality: In high-intensity conflicts today (like the war in Ukraine), we see a "return to attrition" because modern sensors (drones, satellites) make it very difficult to achieve the surprise needed for pure maneuver warfare. When you can see everything, it's hard to be "unexpected."

Can you create an evaluation using this information PHONETICS VS. PHONOLOGY Whereas phonetics is the study of sounds that occur in language, phonology is the study of how these sounds are organized and how they function in language. It uses the classifications of sounds derived from phonetics to describe and analyze how sounds occur in speech. STRUCTURALIST PHONEMICS STRUCTURALIST PHONEMICS As linguists began to study sounds in fine detail, they recognized increasingly complex aspects of phonetic organization. For example, the sound /p/ appears in different varieties in English. STRUCTURALIST PHONEMICS One of the varieties of /p/ is indicated by [ph]. This sound is produced with an accompanying puff of air called aspiration, as in the words “pill,” and “peace.” Another sound, indicated by [p•], is produced when there is little or no aspiration; this sound occurs in a word like “spill.” A third major variety for the /p/ sound is the unreleased [p– ], which may occur at the end of a word like “stop.” To deal with these variations for the /p/ sound, the structuralists suggested the existence of an abstract unit which they termed a phoneme. STRUCTURALIST PHONEMICS A phoneme was defined by the structuralists as an abstract phonological unit that represents a class of real sounds, termed the allophones of a phoneme. The phoneme /p/ in English, then, is represented by the allophones [ph], [p•], and [p– ]. STRUCTURALISTS: MINIMAL PAIRS How do we know what these abstract units of sound called phonemes are? In order to find the phonemes of a language, the structuralists developed the concept of the minimal pair, defined as any two words that: a) Contain the same number of segments b) Differ in meaning c) Exhibit only one phonetic difference. STRUCTURALISTS: MINIMAL PAIRS In practical terms, phonemes distinguish meanings; and a phoneme can also be defined as the smallest meaning-distinguishing unit of sound. For instance, the words “pin” /pɪn/ and “bin” /bɪn/ mean different things, and the only one difference in these words occurs in the initial sounds. STRUCTURALISTS: MINIMAL PAIRS By using the concept of a minimal pair, we can determine that the three variations of the /p/ sound do not represent three phonemes. Certainly, it is possible to pronounce the word cap with either an aspirated [ph ] or unreleased [p– ]; however, the two forms [kæph ] and [kæp– ] are not a minimal pair, even though they involve different sounds, because they are identical in meaning. STRUCTURALISTS: FREE VARIATION The two forms [kæph ] and [kæp– ] are, therefore, said to exhibit free variation: that is, the pronunciation may vary without signifying a change in meaning. In other words, we may conclude that the unreleased [p– ] and the aspirated [ph ] are not representations of different phonemes in English; they are, in fact, allophones of one phoneme, /p/. STRUCTURALISTS: COMPLEMENTARY DISTRIBUTION When phonemes have more than one allophone in a language, the allophones are said to be in complementary distribution. Complementary distribution means that the allophones of a phoneme occur in different phonetic environments (that is, with different sounds surrounding them). TRANSFORMATIONAL- GENERATIVE PHONOLOGY TRANSFORMATIONAL-GENERATIVE PHONOLOGY Transformational-generative phonology is a relatively recent development in linguistic theory. Chomsky launched Transformational-Generative Grammar in 1957, but the earliest studies within this framework were largely concerned with syntax. A decade later, the first comprehensive transformational-generative treatment of English phonology appeared: Chomsky and Halle’s The Sound Pattern of English (1968). TRANSFORMATIONAL-GENERATIVE PHONOLOGY Transformational-generative phonologists strongly oppose the structuralists’ phonemic level. They replace this level by a series of rules that directly relate underlying representations to observed phonetic representations. The central mechanisms in transformational-generative phonology, then, are underlying representations and phonological rules. PHONOLOGICAL RULES A rule is an operational statement in which some linguistic entity is modified, resulting in a new linguistic entity. Rules may add elements, remove elements, or change elements. By using phonological rules, linguists attempt to demonstrate that there is order in linguistic phenomena and that linguistic patterns are systematic. PHONOLOGICAL DERIVATION A phonological derivation is an operation that begins with an underlying representation and, through the application of a set of specific rules, yields the actual sound the speaker produces. The representation of a phonological rule has the following general appearance. /A/ → [B] / C “A” changes to “B” under condition “C” PHONOLOGICAL RULE – EXAMPLE In most Southern dialects, the word ten is pronounced like the word tin. This is not an isolated fact, for den is pronounced like din and Ben is pronounced like bin, and so on. This very general fact can be represented by the phonological rule: /ɛ/ → [I] / ___ [n] den /dɛn/ → /dIn/ Ben /bɛn/ → /bIn/ ten /tɛn/ → /tIn/ /ɛ/ → [I] / ___ [n] - high - low - tense + front + high - tense + front + sonorant + anterior + coronal - continuant NOTATIONAL DEVICES IN PHONOLOGICAL RULES The statement of phonological rules can be complex, and linguists have developed several notational devices for writing them. Often, the following symbols will be necessary for stating the conditions under which rules apply: # indicates a word boundary + indicates an intraword boundary $ indicates a syllable boundary UNDERLYING REPRESENTATIONS AND RELATED ISSUES The transformational-generative description of phonology relates underlying representations to phonetic representations by rules. This can be represented in a simple example: In English, there are certain pairs of words like sign / signature, and malign / malignant that exhibit a regular alternation in their phonetic representations: [g] is present in the second member of the pairs but absent in the first member. UNDERLYING REPRESENTATIONS AND RELATED ISSUES To explain the relatedness of words such as sign / signature, we could claim that the underlying representation of the segment in all such pairs is /g/ and that a rule operates to delete /g/ before syllable-final nasals. Thus, the rule “/g/ is deleted before syllable-final nasal” would appear formally as: + voice - anterior →∅ ____ [+ nasal] $ - coronal UNDERLYING REPRESENTATIONS AND RELATED ISSUES On the left-hand side of the arrow, we place the features needed to uniquely specify /g/ among the consonants; that is, no other consonant has the features [+ voice], [- anterior], and [- coronal]. The symbols → mean that the sound /g/ changes to nothing or more properly “/g/ is deleted.” The horizontal line following the slash mark refers to the position of /g/ - namely, before a segment that is [+nasal]. Finally, this [+nasal] segment occurs before a syllable boundary, as indicated by $. A less formal way of writing this rule would be: /g/ → / _ [+nasal] $ Notice that this rule also helps describe such alternations as phlegm/phlegmatic and paradigm/paradigmatic. Application Activity: Think of other words in which this rule can be applied. Write the sound segments to prove /g/ is deleted. Another example is the process through which the prefix meaning “not” is added to words. This prefix alternates among the forms /Im/, /In/, and /Iŋ/, depending on the point of articulation of the initial segment of the following word. -If the segment begins in the extreme front part of the mouth (labials), the form is /Im/, as in improper. -If the segment begins in the extreme back part of the mouth (velars), the form is /Iŋ/, as in incomplete. -If the segment begins in the mid-region of the mouth (all other sounds), the form is /In/, as in indecent. *Exceptions:Words beginning with /r/ or /l/. Analyze the Word “in + complete,” for example. /n/ → [ŋ] / __ [k] - continuant - continuant - continuant + sonorant → + sonorant - sonorant + anterior - anterior - strident + coronal - coronal - coronal + tense THE VELAR SOFTENING RULE Still another example of alternation in English is found in pairs of words like “electric / electricity,” in which the segments /k/ and /s/ alternate. /k/ changes to [s] only before non- low, front vowels. THE VELAR SOFTENING RULE /k/ → [s] / __ - continuant + continuant - strident → - sonorant V - anterior + anterior - low - coronal + coronal - back

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