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:

Desert Environment

A biome characterized by very little rainfall, extreme temperatures, and sparse vegetation, making it a challenging habitat for life.

Photosynthetic Mode

A method by which plants, algae, and some bacteria convert light energy into chemical energy stored in glucose.

CAM

A type of photosynthesis (Crassulacean Acid Metabolism) adapted by some plants to minimize water loss in arid conditions by fixing CO2 at night.

CAM Plants

Plants that utilize Crassulacean Acid Metabolism, a carbon fixation pathway that allows them to conserve water in arid conditions by opening their stomata at night.