Calculate (a⃗ ×b⃗ )⋅c⃗ for the three vectors a⃗ with magnitude a = 5.14 and angle θa = 23.0 ∘ measured in the sense from the +x - axis toward the +y - axis, b⃗ with b = 4.20 and θb = 63.8 ∘, and c⃗ with magnitude c = 5.96 and in the +z - direction. vectors a⃗ and b⃗ are in the xy-plane.

Mary beth used the mapping rule to find the coordinates of a point that had been rotated 90° counterclockwise around the origin. examine the steps to determine whether she made an error. m (3, –6) is rotated 90° counterclockwise. (x, y) → (–y, x) 1. switch the x- and y-coordinates: (6, –3) 2. multiply the new x-coordinate by –1: (6(–1), –3) 3. simplify: (–6, –3) .

Dexter read 11 science fiction books and 5 history books. lena read 9 science fiction books and 4 history books. compare the students’ ratios of science fiction books to history books. 1. determine the ratios’ form:    science fiction books to history books 2. write the ratios as fractions:    dexter: 115; lena: 94 3. rewrite with a common denominator. 4. compare. 5. answer the question. determine which shows the correct comparison of the ratios for this problem.

Quadrilateral abcd is translated up and to the right, and then rotated about point q. which congruency statement is correct?