Calculate the integral s f · ds, where s is the entire surface of the solid half ball x2 + y2 + z2 ≤ 1, z ≥ 0, and f = (x + 3y5)i + ( y + 10xz)j + (z − xy)k. (let s be oriented by the outward-pointing normal.)

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)