Write the Appropriate Rotation Formulas So That in a Rotated $10 x ^ { 2 } - 4 x y + 6 y ^ { 2 } - 8 x + 8 y = 0$

question 93

Multiple Choice

Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term.
- $10 x ^ { 2 } - 4 x y + 6 y ^ { 2 } - 8 x + 8 y = 0$

• A) \(x = \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 } x ^ { \prime } - \frac { \sqrt { 2 + \sqrt { 2 } } } { 2 } y ^ { \prime } ; y = \frac { \sqrt { 2 + \sqrt { 2 } } } { 2 } x ^ { \prime } + \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 } y ^ { \prime }\)
• B) \(x = \frac { \sqrt { 2 } } { 2 } \left( x ^ { \prime } - y ^ { \prime } \right) ; y = \frac { \sqrt { 2 } } { 2 } \left( x ^ { \prime } + y ^ { \prime } \right)\)
• C) \(x = - y ^ { \prime } ; y = x ^ { \prime }\)
• D) \(x = \frac { 1 } { 2 } x ^ { \prime } - \frac { \sqrt { 3 } } { 2 } y ^ { \prime } ; y = \frac { \sqrt { 3 } } { 2 } x ^ { \prime } + \frac { 1 } { 2 } y ^ { \prime }\)

Understand the basic principles and usages of applets in Java.

Learn the structure and syntax of HTML documents.

Recognize the process of embedding Java applets into HTML pages.

Differentiate between various HTML tags and their functions.

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Definitions:

Purely Competitive Market

A market structure characterized by a large number of small firms, identical products, and free entry and exit, which leads to firms being price takers.

Long-run Equilibrium

A state in which all firms in an industry are making normal profit, with no incentive for new firms to enter or existing firms to leave the market.

Producer Surplus

The difference between what producers are willing to accept for a good or service and the actual price they receive, representing economic gain.

Marginal Cost

The increase in total cost that arises from producing one additional unit of a product or service.