Rotate the Axes to Eliminate The $x y$ -Term in the Following Equation

question 49

Multiple Choice

Rotate the axes to eliminate the $x y$ -term in the following equation. $18 x ^ { 2 } - 12 \sqrt { 3 } x y + 6 y ^ { 2 } + 12 x + 12 \sqrt { 3 } y = 0$

• A) \(\left( y ^ { \prime } \right) ^ { 2 } + x ^ { \prime } = 0\)
• B) \(6 \sqrt { 3 } \left( y ^ { \prime } \right) ^ { 2 } + 6 \sqrt { 3 } x ^ { \prime } = 0\)
• C) \(6 \left( x ^ { \prime } \right) ^ { 2 } - 6 y ^ { \prime } = 0\)
• D) \(\frac { \left( y ^ { \prime } \right) ^ { 2 } } { 6 } + \frac { x ^ { \prime } } { 6 } = 0\)
• E) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 12 } + \frac { y ^ { \prime } } { 12 } = 0\)

Understand the concept and significance of personal and social territories.

Comprehend the principles of equilibrium theory in predicting personal space needs.

Identify the characteristics of third places and their role in social interaction.

Recognize the influence of cultural background on personal space preferences.

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Definitions:

Short-Term

Relating to or occurring on a brief or immediate timescale, typically within one year.

Short-Term Collateralized

Financial arrangements that involve the use of assets as collateral for a short-duration loan.

Repurchase Agreement

A short-term borrowing agreement where one party sells securities and agrees to repurchase them at a higher price at a later date.

Municipal Bond

A bond issued by local or state governments to finance public projects, often offering tax-exempt interest payments.