5. Найдите угол между векторами \(\mathbf{a}(1; 3)\) и \(\mathbf{b}(2; 1)\).

\(\mathbf{a} \cdot \mathbf{b} = 1 \cdot 2 + 3 \cdot 1 = 2 + 3 = 5\). \(\|\mathbf{a}\| = \sqrt{1^2 + 3^2} = \sqrt{10}\), \(\|\mathbf{b}\| = \sqrt{2^2 + 1^2} = \sqrt{5}\). \(\cos \theta = \frac{5}{\sqrt{10} \cdot \sqrt{5}} = \frac{5}{\sqrt{50}} = \frac{5}{5\sqrt{2}} = \frac{1}{\sqrt{2}}\). \(\theta = 45^\circ\). Ответ: \(в\).