7 Let v 35 and w 4 13 Find the rotation matrix Rtheta that

(7) Let v = (3.5) and w = (-4, -1/3). Find the rotation matrix, R(theta) that Will rotate v into w.

v = (3,5)

means, r1 = sqrt( 3^2 + 5^2) = 5.831

theta(1) = arc tan(5/3) = 59.03 deg.

w = (-4,-1/3)

means r2 = sqrt((-4)^2 + (-1/3)^2) = 4.014

theta(2) = 180 + arc ( 1/12) = 180 + 4.76 = 184.76 deg.

So,

rotation matrix will be,

r = sqrt((r₁^2 + r₂^2)/2) = 5.005

theta = (theta1+theta2)/2 = 121.90