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Unformatted text preview: s to a point rotated 45◦ counterclockwise from P where R= √
2 √ − 2
2 (a) Find R−1 .
(b) If RP rotates a point counterclockwise 45◦ , what should R−1 P do? Check your answer
by ﬁnding R−1 P for various points on the coordinate axes and the lines y = x and
y = −x.
(c) Find R−1 P where P corresponds to a generic point P (x, y ). Verify that this takes points
on the curve y = x to points on the curve x2 − y 2 = 4. 506 Systems of Equations and Matrices 5. A Sasquatch’s diet consists of three primary foods: Ippizuti Fish, Misty Mushrooms, and Sun
Berries. Each serving of Ippizuti Fish is 500 calories, contains 40 grams of protein, and has
no Vitamin X. Each serving of Misty Mushrooms is 50 calories, contains 1 gram of protein,
and 5 milligrams of Vitamin X. Finally, each serving of Sun Berries is 80 calories, contains
no protein, but has 15 milligrams of Vitamin X.9
(a) If an adult male Sasquatch requires 3200 calories, 130 grams of protein, and 275 milligrams of Vitamin X daily, use a matrix inverse to ﬁnd h...
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