In triangle ABC, suppose you are given the measures of \angle A , \angle B , and the length of side a (opposite \angle A ). Which of the following must always be true for these given values?

The sum of \angle A and \angle B must be less than 180^\circ .

You can always use the Pythagorean Theorem to find the missing side.

\angle A and \angle B must be equal to each other.

Side a must be the longest side of triangle ABC.

Arrange these terms to form a logical mathematical equation related to triangle sides and angles.

\frac{a}{\sin A} ,equals, \frac{b}{\sin B} , \frac{c}{\sin C}

In triangle $ABC$, you are given that side $a = 7$ units, side $b = 10$ units, and angle $A = 40^\circ$. Before applying the Law of Sines to solve for angle $B$, what knowledge or skills must you already have from earlier math topics?

Being familiar with how to convert degrees to radians.

Knowing the Law of Sines formula: $\frac{a}{\sin A} = \frac{b}{\sin B}$.

Knowing the Pythagorean Theorem applies to all triangles.

Applications of the Law of Sines in Real Life - Starter Quiz

Applications of the Law of Cosines in Geometry - Starter Quiz

Electrostatics The section of CBSE Class 12 Physics electrostatic potential and capacitance notes mainly deals with the in-depth analysis of electromagnetic phenomena when they are not performing any movements. Additionally, it is divided into ten further sub-topics to study the companion processes of reaching the state. These are - 1. Electric charge In this section of Physics ch 2 Class 12 notes, you get to learn about the basic features of electric charge and its expression in Physics. Along with its basics, the sections help to understand the full potential of charge. Different aspects of Charge included in Class 12 Physics Chapter 2 notes are - Definition Type: Positive and Negative Charge Unit and dimensional formula Point Charge Properties of Charge Comparison of Charge and Mass Methods of Charging Electroscope 2. Coulomb's Law Force is created when charges of opposite signs attract each other, and they repulse if the signs are the same. Coulomb's law tries to define this phenomenon through a mathematical formula, explicitly mentioned in Physics Class 12 notes Chapter 2. Moreover, there is key information about the variation of the constant k and its effect on a medium. Coulomb's law's vector form and the principle of superimposition are also explained in ch 2 Physics Class 12 notes. (Image will be uploaded soon) 3. Electric Field As stated in Class 12 Physics Chapter 2 notes, every positively or negatively charged particle has their respective electric fields. It feels a force at the time of interaction which might be attraction or repulsion. As it arises from electric charge, it is crucial to know about its different parts like - Electric field intensity Relation between electric force and electric field Super imposition of electric field Point charge Continuous charge distributions Properties of Electric Field Lines Motion of Charged Particles in an Electric field Learning more about the electric field from electric potential and capacitance notes Class 12 helps a student to get a grasp of upcoming chapters. 4. Electric Potential Energy When energy helps a charge to move from an electric field, it is known as the Electric Potential Energy. This section of electrostatic chapter Class 12 notes requires a student to study the Electron volt (eV), and the potential energy that an n number of charges can hold. 5. Electric Potential This section of Class 12 Physics Chapter 2 notes focuses on in-depth learning of Electric Potential or Voltage. Basically, it defines the potential movement of energy. 6. Relation between Electric Field and Potential Apart from knowing more about the relationship between the two values, Physics Class 12 Chapter 2 notes also discuss equipotential surfaces. 7. Electric Dipole Essentially, 'Dipoles' are two opposite points of charge represented with q and –q, with their distance between each other being 2a. Electric Dipoles are crucial in your study of Physics Class 12 Chapter 2 notes to learn more about electric fields and their potential. Additionally, Class 12 Physics Chapter 2 notes focus on the influence of electric dipoles on a uniform electric field mainly through Force and Torque, Work, and Potential Energy. In the last part of Electrostatics, further focus is on using the formulas to their fullest potential. It includes subsections of Electric Field, Electric Potential Energy, Electric Potential, and Electric Dipole. In the notes for electrostatic potential and capacitance, you will find proper solutions accompanied by clear and crisp diagrams for better understanding. 8. Gauss's Law Apart from just discussing the Gauss's Law, in Physics Class 12 ch 2 notes there is a thorough explanation of its properties and applications. The Gauss' Law states that net electric flux passing through a hypothetical closed surface is equal to the net electric charge present within the same closed surface. Being a broad part of the whole chapter, you may need to spend a little more time on it. Moving forward, it starts discussing the properties of conductors in relation to Gauss's Law. The Class 12 Physics notes Chapter 2 perfectly defines the journey to Gauss' Law from Coulomb's Law. Here is the Gauss's Law present in the Class 12 Physics ch 2 notes, (image will be uploaded soon) 9. Capacitors There is a dedicated section about Capacitors in the Class 12 Physics Chapter 2 notes elucidating its functions and importance as storage of potential electric energy. After explaining the structure of a capacitor, it points out the different types, parallel plate, spherical and cylindrical. The section of Chapter 2 notes of Physics Class 12 is further divided into subheads like: Properties of an ideal battery Grouping of capacitors Simple circuits (Series and Parallel) Dielectric Van de Graaff generator Combination of drops Charge distribution method Wheatstone Bridge-based circuit Extended Wheatstone Bridge Infinite network of capacitors Redistribution of charge between two capacitors Vedantu prepares the Class 12 Physics Chapter 2 notes with help from subject matter experts. In the PDF, you get a comprehensive idea of the topic along with potential answers to the most asked questions. Furthermore, the detailed explanation on each section and subsections are written in a simple language allows a student to ace their exams with wholesome knowledge. These Physics Chapter 2 Class 12 notes are going to be one of the best supplementary study materials besides a student’s textbooks. Visit the Vedantu website or download the app to get your hands on all important notes! Important Questions A charge of 4 × 10–8C is uniformly distributed on the surface of a spherical conductor, having a radius of 15 cm. Determine the electric field just outside this sphere at a point that is 15 cm from the centre of this sphere. Determine the capacitance given that the distance between the two plates has been reduced by half and the parallel plate capacitor holds a capacitance of 20 pF (where 1pF = 10-12 F) having air between the two plates. What will be the total capacitance of a combination where three capacitors, each having a capacitance of 20 pF, are connected in series. A square having a side of 10 cm has a 500 µC charge at its centre. Determine the work done to move a charge of 10 µC between two points that are diagonally opposite each other on the square. At an equatorial point, what will be the electrostatic potential because of an electric dipole? Calculate the work done to move a test charge, q, through a length of 1 cm along the equatorial axis of an electric dipole? Polarisation A capacitor has its plates enclosed in a medium that can be filled by insulating substances. A net dipole moment is then induced by an electric field in the dielectric. This event causes the field in an opposite direction. Equipotential Surface An equipotential surface is a type of surface where the potential always has a constant value. If considered as a point charge, the concentric spheres that are centred at a particular area of this charge are basically equipotential surfaces. Advantages of Vedantu's Revision Notes: A Comprehensive Resource for Effective Learning There are several reasons why one may refer to Vedantu's revision notes for studying a subject like Electrostatic Potential and Capacitance. Here are some key points: Comprehensive Coverage: Vedantu's revision notes provide a comprehensive coverage of the entire topic, ensuring that all important concepts and subtopics are included. Concise and Organized: The notes are designed to be concise, focusing on the key points and core ideas. They are organized in a structured manner, making it easy for students to navigate and revise the content. Simplified Explanation: The revision notes offer simplified explanations of complex concepts, making them more accessible and easier to understand. This helps students grasp the material more effectively. Key Formulas and Equations: The notes highlight the key formulas and equations relevant to the topic, ensuring that students have a clear understanding of the mathematical aspects of Electrostatic Potential and Capacitance. Examples and Illustrations: Vedantu's revision notes often include examples and illustrations that help clarify concepts and provide practical applications, enabling students to better relate theory to real-world scenarios. Quick Recap: The revision notes serve as a quick recap of the important points, allowing students to review the material efficiently before exams or assessments. Exam-Oriented Approach: Vedantu's revision notes are designed with an exam-oriented approach, focusing on the topics and concepts that are frequently asked in examinations. This helps students prepare effectively and increase their chances of scoring well. Accessible Anytime: Vedantu's revision notes are easily accessible online, allowing students to study at their convenience and revise the material anytime, anywhere.

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."

What is a crime A crime is generally defined as an act or omission that is prohibited by criminal law Two critical ingredients of a crime are: 1) the commission of an act (Actus reus) 2) the mental intent to commit the act (Mens rea) A crime occurs when a person Commits an act or fails to commit an act when under a legal responsibility to do so Has the intent or mens rea to commit the act Does not have a legal defence or justification for committing the act and Violates a provision in criminal law The Social construction of crime Important to distinguish between behaviours that may be considered deviant by society and crimes Deviance is behaviour that is contrary to the norms and values of the larger society Crime is behaviour that breaks the law Deviance includes: Criminal behaviour and Wide range of other behaviours not against the law: May be frowned upon by the larger society What is viewed as deviant changes over time Crime includes: Social construction of crime Legal status of behaviours is not determined by behaviour itself but result of social response to the behaviour/persons/groups engaged in it Criminologists often conduct historical analyses to understand how social, economic and political environments may influence legislation Moral entrepreneurs Often play a key role in criminalizing certain activities Individuals, groups or organizations, seek action against certain groups of people/behaviours and bring pressure on legislators to enact criminal statutes The Origins and Application of the Criminal Law Differing perspectives on where criminal laws come from/ applied via the criminal justice system are reflected in two models 1) Value consensus model 2) Conflict Model Value consensus model Behaviours are defined as criminal/punishment imposed, reflect opinions/limits of tolerance Application of law, society reaffirms acceptable behaviours/social cohesion Conflict Model Crime and punishment reflect the power some groups have to influence, formulation/application of criminal law rich/privileged have an advantage in influencing law reform/criminal justice system The Canadian Legal System Is a common law system, with exception of Quebec which has a civil law system (Based on the French Code Napoleon) Common law is law based on custom, tradition, practice and generally unwritten Precedent is a judicial decision may be use as a standard in subsequent similar cases Canadian Courts Canadian courts organised in a hierarchy Supreme court of Canada is the highest court Stare decisis- principle whereby higher courts set precedents that lower courts must follow “To stand by what was decided” Like cases should be treated alike All courts below SSC bound to apply that same ruling in subsequent cases Criminal Law Body of law deals with conduct considered so harmful to society as a whole that it is prohibited by statute and prosecuted and punished by the government Functions of the Criminal Law In Canadian society, Criminal law provides the following functions Acts as a mechanism of social control Defines the parameters of acceptable behaviour Reduces the risk of personal retaliation Assists in general and specific deterrence Prosecutes criminalized behaviour Protects groups interests Principles of Canadian Law The Rule of Law The requirement that governments as well as individuals be subjected to Traced back to the English Magna Carta The essence of the rule of law is that No one person is above the law All persons are bound by the law All are entitled to protection by the law The law should be observed and enforced equally There is a standard to which criminal justice officials must adhere and will be held accountable Criminal Law Vs. Civil (Tort) Law Summary Crime is a social construction and is a reflection of changing time and mores Criminal law is not static and what behaviour legislatively defined as criminal can change overnight There are instances in which controversy arises when the criminal law is applied to issues of ethics, morality and religion The criminal law was identified as one type of public law and the functions of the criminal law were set out The rule of law and the charter of rights and freedoms are two key parts of the foundation of the criminal justice system There are several principles that also provide the foundation for Canadian law The role, principles origins and application of the criminal law were examined and a number of case studies were presented to illustrate the dynamic nature of the criminal law in a diverse society

History of policing Pre-confederation Mostly informal policing by community residents First police officers Quebec city, mid 17th century Upper Canada, early 19th century Mandate Police conflicts between ethinc groups and employes/labours Maintain moral standards (drunkenness, alcoholism) Apprehend criminals Provincal Police Force Response to disorder resulting form gold strikes in 19th century Replaced by RCMP during 20th century Currently, Ontario,Quebec and parts of Newfoundland have their own provincal police force History of RCMP North-Wesr Mounted Police Founded in 1873 Maintain law and order Ensure orderly settlement in prairies Many problems: desertion, resignation and improper conduct Replaced by Royal Canadain Mounted Police Police Today About 70,000 police officers across Canada 199 police officers per 100,000 population Lower than Scotland (337), England(244), U.S (238) NUmber increased over past decade NUmber of female officers increased 1 out of 5 officers is a women Contemporary Policing Structure of policing Four levels Federal, Provincial, municipal, and First nations Also public transportation police (railway, airport, and transit) Some municipalities have own forces E.g, Peel, Toronoto Others use provincial force detachments or RCMP detachments Royal Candanin Mounted Police Governed by Royal Canadian Mounted Pollcei Act (1985) Broad Range of policing activities, including federal policing and international peacekeppiong Contract Policing Provincial, territorial and municipal level Concerns about local oversight and accountability In but not of communities-difficult to ensure that RCMp detachments are responsive to communities Provincial Police Three forces Ontario Provincial Police Surete du Quebec (SQ) Royal Newfoundland Constabulary (RNC) Other provinces contractually use the RCMP Responsibilities Police rural areas and areas outside municipalities Enforce provincial laws and Criminal Code Regional Police Amalgamated Forces E.g Peel region police and Halton Regional Police Force Provide Police Services to over Half of Ontarians Advantages Cheaper, more servies Disadvantages To centralized, not in touch with community Municipal Police Responsibilites Enforce Criminal Code, Provincal Statues, municipal by laws, some federal statues (e.g drugs) Largest number of officers of any level My be contracted to RCMP or Provincal force Costs are paid by the municipality First Nations Type of policing is negotiated by First Nations Commnity Autonomous reserve based First Nations Officers from RCMP or OPP Responsibilites Enforce Criminal Code, federal and provicanl statues, band bylaws Accountability Reserve based police commission or band council Private Security Services Two main types 1. Private Security Firms 2. Company based, in house security officers No more legal authority than ordinary citizens But can arrest and detain people who commit crimes on private property In Canada, Private security officers outnumber police officer by four to one Parapolice Extension of activities Lack of systems of oversight like transitional police Police Work POlicing The activities of any indivual or organization acting legally on behalf of public or private organizations or persons to maintain security or social order Pluralization of Policing The sharing between public and private security Legislative Framework Carry out tasks within a number of legislative frameworks, define role, powers/responsibilites Canadian charter of rights and freedoms- most impactful on power/actvites of police Provincial and municipal legislation - Status such as motor vehicle administration acts, highway traffic acts, liquor acts and provincial/musincpal police acts Democracy Governance Categories of Policing Recruitment and Training of police officers Police recruitment Recruiting Visible Minorites and Aboriginal People Special initvates and programs for youth, women and visible minorities PEACE (Police Ethnic and Cultureal Exchange) OPPBound (particpate in variety of activate with officer) Toronto POlice recruitment of Somali Officers Edmonton police uniforms that include a hijab Police Training Residential/non-residential academies, centralized and decentralized Physical and academic instruction, socilization into the police occupation Operational field traiing Hands-on application of principles learned in the academy Mentoship form senior officer Working Personality of Police officers Challenges of Police Work Work Enviroment Long hours and shift work Exposure to stressors, especially in high demand environments PTSD and burnout Work Organiztion Harassment of female officers Cumbersome of system of internal redress Summary A number of misconceptions arounds police work, including th emotion that most police work involves crime control A variety of influences on the roles and activities of the police Four levels of policing: federal, provincial, mnicipal and First Nations, each with different responsibilities

Extradition (International law), Political Offence Exception, The Political Offense Exception (POE) serves as a critical safeguard in international extradition law, allowing a requested state to refuse the surrender of a fugitive if their alleged crime is of a "political character." These offenses are categorized into two types: **pure political offenses**, such as treason or espionage, which target the state's political organization without harming individuals; and **relative political offenses**, which are common crimes like robbery committed with a political motive. To distinguish between these, courts apply various judicial tests. For instance, the **Political Incidence Test** (established in *In re Castioni*) focuses on whether the act was incidental to a political disturbance, while the **Swiss Proportionality Test** weighs the political end against the criminal means used, denying the exception if the harm caused is disproportionate. In the context of **state succession**, the application of extradition treaties depends largely on the underlying legal theory adopted by the new sovereign. Under **Universal Succession**, the new state inherits all prior treaties and obligations, ensuring legal continuity. Conversely, the **Clean Slate (Tabula Rasa) Theory**, often seen in decolonization, suggests that new states are not bound by the predecessor’s treaties, potentially creating "safe havens" for fugitives until new agreements are reached. Practical examples include the **Dissolution of the USSR**, where Russia acted as the "continuator" state inheriting treaties, and the **Partition of India and Pakistan**, where a devolution agreement ensured that colonial-era treaties remained in effect. Despite its protective intent, the POE faces **modern erosion** to ensure that heinous acts do not go unpunished. Specific limitations, such as the **Attentat Clause**, explicitly exclude the assassination of a head of state from being considered a political offense. Similarly, modern treaties and conventions (like the *Meunier* ruling) exclude **terrorism**, hijacking, and crimes against humanity from the exception, viewing these acts as attacks on the general social order rather than legitimate political dissent. This evolution reflects a growing international consensus that the gravity of certain crimes—such as those seen in the **Rainbow Warrior case study**—far outweighs any claimed political motivation, shifting the legal focus toward human rights and the prevention of torture.

Short Quiz in Science 10 cite examples of practical applications of the different regions of EM waves, such as the use of radio waves in telecommunications;

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