1. Given the following propositions:
(1) If $a^{2} x>a^{2} y$, then $x>y$;
(2) If $a^{2} x \geqslant a^{2} y$, then $x \geqslant y$;
(3) If $\frac{x}{a^{2}} \geqslant \frac{y}{a^{2}}$, then $x \geqslant y$;
(4) If $x \geqslant y$, then $\frac{x}{a^{2}} \geqslant \frac{y}{a^{2}}$.

Among them, the number of correct propositions is ( ).
(A) 1
(B) 2
(C) 3
(D) 4
- 1. B.

In propositions (1) and (3), $a \neq 0, a^{2}>0$, holds;
In proposition (2), $a$ can be 0, take $x=-1, y=0$, $a=0$, does not hold;
In proposition (4), $a$ can be 0, does not hold.