Chapter 7 - Section 7.6 - Vectors: The Dot Product - 7.6 Problem Set - Page 411: 26

$81.1^\circ$.

From what we learned: $\cos\theta=\frac{U\cdot V}{|U||V|}=\frac{4\cdot7+5\cdot(-4)}{\sqrt{(4^2+5^2}\sqrt{7^2+(-4)^2}}=\frac{8}{\sqrt{41}\cdot\sqrt{65}}=\frac{8}{\sqrt{2665}}$ Thus $\theta=\cos^{-1}\frac{8}{\sqrt{2665}}\approx81.1^\circ$.