Determine the Appropriate Rotation Formulas to Use So That the New

question 17

Multiple Choice

Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.
- $$4 x ^ { 2 } + 6 x y + 4 y ^ { 2 } - 8 x + 8 y = 0$$

• A) \(x = \frac { u } { \sqrt { 2 } } - \frac { v } { \sqrt { 2 } }\) and \(y = \frac { u } { \sqrt { 2 } } + \frac { v } { \sqrt { 2 } }\)
• B) \(x = \frac { 1 } { 2 } u - \frac { \sqrt { 3 } } { 2 } v\) and \(y = \frac { \sqrt { 3 } } { 2 } u + \frac { 1 } { 2 } v\)
• C) \(x = - v\) and \(y = u\)
• D) \(x = \frac { u } { \sqrt { 2 } } + \frac { v } { \sqrt { 2 } }\) and \(y = \frac { u } { \sqrt { 2 } } - \frac { v } { \sqrt { 2 } }\)

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Definitions:

Milgram Experiment

A psychological experiment conducted by Stanley Milgram in the 1960s to study obedience to authority, where participants were instructed to administer electric shocks to another person.

Stanford University Prison Experiment

A psychological study conducted by Philip Zimbardo in 1971 at Stanford University, where students were assigned roles of prisoners and guards to explore the effects of perceived power.

Generalization

Drawing a conclusion about a certain characteristic of a population based on a sample from it.

Logical Support

The provision of reasons or evidence to justify a claim or argument.