For each of the matrices in Exercises 1 through 6, find an orthonormal eigenbasis. Do not use technology.

L6 - 11 Now You Try It (NYTI): The position function of a ball throw into the air with a velocityf0fsci 2 given by H(t)=4 0 t−16t where H(t)i sheegtofhealboetherund after t seconds. (a) Find the average velocity of the ball on the interval starting with t =2to the time 0.5sodsl,adtenealohei e0 .1ondl. (b) Now write an expression for the average velocity of the ball on the time interval from t =2to h seconds later, i.e. on the interval [2,2+ h], where h .=0 (c) What happens as h gets closer and closer to 0 (d) Find the instantaneous velocity of the ball when t =2 .