2. If $a_{1}, a_{2}, \cdots, a_{n}$ is a set of real numbers, and $a_{1}+a_{2}+\cdots+a_{n}=k$. Find the minimum value of $a_{1}^{2}+a_{2}^{2}+\cdots+a_{n}^{2}$.
2. $f(x)=x^{2}$ is a convex function on $(-\infty,+\infty)$, so $\frac{1}{n}\left[f\left(a_{1}\right)+\cdots+f\left(a_{n}\right)\right] \geqslant f\left(\frac{a_{1}+\cdots+a_{n}}{n}\right)$. Therefore, $a_{1}^{2}+a_{2}^{2}+\cdots+a_{n}^{2} \geqslant n \cdot\left(\frac{k}{n}\right)^{2}=\frac{k^{2}}{n}$.
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