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The process of splitting a vector into two or more vectors in such a way that their combined effect is same as that of the given vector called-
  • a)
    Resolution of Vector
  • b)
    Unit vector
  • c)
    Uniqueness of resolution
  • d)
    None of the above
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The process of splitting a vector into two or more vectors in such a w...
Concept:
  • Resolution of vectors is the process of splitting a vector into two or more vectors in such a way that their combined effect is the same as that of the given vectors.
    • The vectors into which the given vector is split are called Components of vectors.
Explanation:
  • Resolution of vectors into components: We have a vector (F) where the magnitude of the vector is F and the angle with horizontal is θ.
The vector has two components: 1. Vertical component and 2. Horizontal component
Vertical component (Fy) = F Sinθ
Horizontal component (Fx) = F Cosθ 
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In its refined form, iron is a shiny, silver-gray metal; however, when refined iron is exposed to atmospheric conditions for an extended period of time, its surface becomes flaky, pitted, and red- or orange-colored. This process is known as "rusting," and the new flaky, orange or red substance is called "rust."Below, two scientists discuss how rust forms and the composition of rust.Scientist 1:Both water and oxygen are needed for rust to form. Water is an electrolyte, meaning that it allows ions to move within it. When iron comes into contact with water, some iron naturally dissociates into iron ions (Fe2+) and free electrons. Additionally, when atmospheric oxygen (O2) dissolves in water, some oxygen reacts with water to form hydroxide ions (OH-). Because water allows ions to move freely, iron ions and hydroxide ions combine to form a new compound: iron hydroxide. However, iron hydroxide is not a stable compound. Over time, as water evaporates, it changes into a hydrated form of iron oxide. This is rust.Salts can act as catalysts for rust formation, meaning that they speed up the rate at which rust forms. However, rust can form in pure water, in the absence of added salts.Increasing the ambient temperature increases the rate of rust formation. Additionally, increasing the amount of irons surface area that is exposed to water also increases the rate at which rust forms. However, because a layer of rust is porous to water and oxygen, water and oxygen will continue to cause the interior of a piece of iron to rust even after the irons surface has been rusted.Scientist 2:Attack by acids causes rust to form. In water, acids ionize to create positively-charged hydronium (H+) ions and negatively-charged anions. Hydronium ions are electron-deficient; because of this, they attract electrons from iron. This creates iron ions (Fe2+), which are soluble in water. Once dissolved in water, iron ions react with dissolved atmospheric oxygen (O2) to create iron oxide, or rust.Acids can come from a variety of sources. For example, when carbon dioxide in the atmosphere dissolves in water, carbonic acid (H2CO3) is created. Carbonic acid is the most common cause of rusting. However, other environmental sources of acids exist. Rainwater is normally slightly acidic because it has come into contact with molecules in the atmosphere, like sulfur dioxide and nitrogen oxides. These molecules also dissolve in water to form acids. Additionally, iron itself may contain impurities such as phosphorous and sulfur, which react with water to produce acids. Both acidic environments and impurities within iron itself create the conditions under which iron rusts.Rusting can be prevented by painting the surface of iron, thus preventing it from coming into contact with water, oxygen, and acids. Iron can also be protected in a process called "galvanizing," which involves coating iron in a thin layer of zinc. Because zinc is more reactive than iron, it is corroded while the iron is protected.Q. Given that all of the following are true, which of the following, if found, provides the strongest evidence against Scientist 1s hypothesis?

Directions:In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will find alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also find questions about a particular section of the passage, or about the entire passage. These questions will be identified either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.PassagePuzzling NumbersThe Japanese number game Sudoku has taken the world (1) with storm. While crossword puzzles seem to be the game of choice, (2) they need only sit in an airport or doctor’s office in any city to see how Sudoku is slowly overtaking the popular word game.In the most common game of Sudoku, the player is faced with a nine-by-nine space grid with a total of 81 spaces. The solution to the puzzle requires a number, one through nine, to be placed in each box. (3) Each number must appear only once in each row and only once in each column. A Sudoku puzzle will begin with a few digits already in place. The solver’s (4) task, is to figure out which numeral belongs in the remaining empty spaces. While being a math whiz is no requirement for this seemingly simple process, a level of logic and reasoning (5) is necessary in order to choose the correct number for each space. As with most such activities, practice makes perfect with Sudoku. The puzzles that seem impossible at first glance (6) eventual become more manageable.The name Sudoku is derived from the phrase single number in the Japanese language. (7) Nevertheless, its definition refers to the placement or allotment of a single number. This puzzle is aptly (8) named, since the misplacement of a single number spells the beginning of an incorrect solution. For this reason, Sudoku (9) should have been played using a pencil with a good eraser.It is nearly impossible to discern (10) which number the solver has placed incorrectly once an error is discovered. If you don’t have a pencil, use a pen to write the digit as a series of light dots. This way, (11) should you make a mistake, you can retrace your steps to locate and correct the original errant placement.There are certain strategies involved in solving a Sudoku puzzle, including the process of elimination. For example, if a row of nine spaces already has the number 4, that row cannot contain another 4. This goes for columns as well. The solver can use these clues and a bit of deduction to limit the possible combinations of numbers. By attacking the puzzle using (12) logic, you can turn the process into an amusing challenge rather than an impossible task.1. The origin of Sudoku is attributed to Leonhard Euler, the Swiss mathematician who (13) sometimes developed the game Magic Squares in 1783.2. In fact, Euler’s game was actually based on a game derived from Chinese folklore.3. The primary difference between Magic Squares and Sudoku is that Euler’s game has no grid dividing the puzzle and it is somewhat easier to solve, since there are multiple possibilities for a solution.4.In true Sudoku, each puzzle has only one solution.5. The puzzle’s difficulty varies according to the number of digits that are initially provided.6. When faced with a puzzle with only one 3 provided, for example, you can be sure that it will be more difficult to solve than a puzzle that already has half of the numbers placed in the correct boxes. (14)One has only to examine a local newspaper to ascertain the popularity of this addictive brain teaser. Where comics and crossword puzzles reign supreme, it is often easy to locate a grid of spaces and numbers tucked off in a corner, or even sitting boldly next to the time-honored crossword.Q. (14)If the writer were to divide the preceding paragraph into two shorter paragraphs in order to differentiate between the origin and evolution of the game and the difficulty of playing the game, the new paragraph should begin with Sentence

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The process of splitting a vector into two or more vectors in such a way that their combined effect is same as that of the given vector called-a)Resolution of Vectorb)Unit vectorc)Uniqueness of resolutiond)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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