Find real numbers a and b so that the transformation l(x, y) = (aa− b, b+ aa) produces the specified rotation
and dilation.
a. rotation by 270° counterclockwise and dilation by scale factor 1/2.
b. rotation by 135° counterclockwise and dilation by scale factor √2.
c. rotation by 45° clockwise and dilation by scale factor 10.
d. rotation by 540° counterclockwise and dilation by scale factor 4.

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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