Solution: The angle $\theta$ between $\mathbfa$ and $\mathbfb$ is given by $\cos\theta = \frac{\mathbfa \cdot \mathbfb}{\|\mathbfa\| \|\mathbfb\|}$. Compute the dot product: $2(1) + (-3)(4) = 2 - 12 = -10$. Compute magnitudes: $\|\mathbfa\| = \sqrt2^2 + (-3)^2 = \sqrt13$, $\|\mathbfb\| = \sqrt1^2 + 4^2 = \sqrt17$. Thus, $\cos\theta = \frac-10{\sqrt13\sqrt17}$. Rationalizing, $\theta = \arccos\left(-\frac10{\sqrt221}\right)$. $\boxed{\arccos\left(-\dfrac10{\sqrt221}\right)}$ - Silent Sales Machine