Let a be real symmetric and positive semidefinite. let α1 ≤ · · · ≤ αn be the eigenvalues of a. show that for any nonzero vector x ∈ rn, we have α1 ≤ ila xll / xll ≤ αn.

Michael gose to a theme park and rides two different roller coasters that both begin on a raised platform his height while on the first roller coaster measured in feet from the platform height can be modeled by the following graph where t is the number of seconds since the ride began