Determine the Appropriate Rotation Formulas to Use So That the New

question 16

Multiple Choice

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

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

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Definitions:

Cold Fusion

A hypothetical type of nuclear reaction that would occur at, or near, room temperature, compared to the high temperatures required for traditional nuclear fusion.

Probability

A measure of the likelihood that an event will occur, often expressed as a number between 0 and 1.

Probability

A measure of the likelihood that an event will occur, expressed as a number between 0 (impossibility) and 1 (certainty).

Notation P(A)

In probability theory, a notation representing the probability of event A occurring.