(1, 0, 0) is mapped to (0, 1, 0), (0, 1, 0) is mapped to (-1, 0, 0), and (0, 0, -1). Geometrically, a three dimensional figure is rotated 90 degrees...
The more people you have the less time it will take. This is an "inverse" proportion. You have 4/10= 2/5 as many people so it will take 10/4= 5/2 as...
Since f(x)= x if x\le 0 and f(x)= x+ 1 if x> 0, xf(x)= x^2 if x\le 0 and xf(x)= x^2+ x if x> 0. So \int_{-2}^1 xf(x)dx= \int_{-2}^0 x^2 dx+ \int_0^1...