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

question 38

Multiple Choice

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

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

Distinguish between absolute and comparative advantage in trade relationships.

Recognize the conditions under which economies or individuals can benefit from trade, even when one party is more efficient in all areas of production.

Identify how opportunity costs shift the production possibilities frontier and influence economic choices.

Understand the limitations and potential of an economy to produce within and outside its production possibilities frontier.

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Definitions:

Thinking At The Margin

The concept involves making decisions based on the additional benefit or cost of the next unit of production or consumption.

Air Travel

The act of moving from one place to another through the atmosphere, typically using airplanes or other aircraft.

Bus Ticket

A document or electronic confirmation that permits a person to travel on a bus.

Comparative Advantage

is the ability of an entity to produce a good or service at a lower opportunity cost than others, leading to trade benefits.