1. Given the sets
$$
A=\left\{1,2, \frac{1}{2}\right\}, B=\left\{y \mid y=x^{2}, x \in A\right\} \text {. }
$$

Then $A \cap B=(\quad)$.
(A) $\left\{\frac{1}{2}\right\}$
(B) $\{2\}$
(C) $\{1\}$
(D) $\varnothing$
$-1 . \mathrm{C.}$
From the problem, we know that $B=\left\{1,4, \frac{1}{4}\right\}$. Therefore, $A \cap B=\{1\}$.