Let f : R [0, ) be an integrable function with compact support. View f as defining the mass density of a rigid body B, which is the support of f, as follows: for any compact set K CR, the mass of Kn B is Let r = (K) = []], f(x, y, z) dxdydz. K (x, y, z) denote the position vector in R. Define the inertia tensor I : R R by I(u) = SSSB rx (ur)f(x, y, z) dxdydz. Prove that I has the following properties: (1) I is a linear transformation. (2) For all u R, u. I(u) 0. (3) For all u, v R, u I(v) = v I(u).