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 \(\mathrm { y } = \frac { \mathrm { u } } { \sqrt { 2 } } + \frac { \mathrm { v } } { \sqrt { 2 } }\)

Distinguish between universal and particular statements.

Identify affirmative and negative statements.

Comprehend open and closed sentences in logical expressions.

Recognize free and bound variables in logical sentences.

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Definitions:

Stock Split

A corporate action in which a company divides its existing shares into multiple shares to boost the liquidity of the shares, making them more affordable to small investors.

Shares

Shares represent units of ownership interest in a corporation or financial asset, providing shareholders with a proportion of the company's profits and a claim on assets.

Earnings Per Share

A financial metric calculated as a company's net income divided by the number of outstanding shares, indicating the profitability per share.

Preferred Stock

A class of ownership in a corporation that has a higher claim on assets and earnings than common stock, typically with fixed dividends.