The lightest solid material is silica aerogel, which has a typical density of only about 0.10 g/cm3. The molecular structure of silica aerogel is typically empty space. What is the mass of 5 m3 of silica aerogel?

Astone weighing 1.5 kilograms is resting on a rock at a height of 20 meters above the ground. the stone rolls down 10 meters and comes to rest on a patch of moss. the gravitational potential energy of the stone on the moss is joules.

Consider a system with two masses that are moving away from each other. why will the kinetic energy differ if the frame of reference is a stationary observer or one of the masses?

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k