(7) If the parabola $y=p x^{2}$ intersects with the square whose vertices are $A(1,1)$, $B(2,1)$, $C(2,2)$, and $D(1$, 2), then the range of the real number $p$ is $\qquad$.
(7) $\left[\frac{1}{4}, 2\right]$ Hint: From the parabola $y=p x^{2}$ passing through $B(2,1)$ and $D(1,2)$, we get $p=\frac{1}{4}$ and $p=2$, respectively, then $\frac{1}{4} \leqslant p \leqslant 2$.