The second hand of a clock is 8 cm long. Find the linear speed of the tip of this second hand as it passes the clock face.]

While goofing off at the ice skating rink, a student takes off her shoes and places each of them on the ice. her friend, a hockey player, then shoots a hockey puck at each shoe. the first puck immediately comes to rest after it collides with the left shoe. the second puck rebounds after it collides with the right shoe. if each hockey puck has the same incoming speed, which shoe has greater speed after the collision? the right shoe. both shoes have the same speed. the left shoe.

What object a collides with object b and bounces back its final momentum is?

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