7.10 Let $\sin 10^{\circ}-\cos 10^{\circ}=a$, among the following three expressions:
(1) $3 a>2 a$;
(2) $\log _{(-a)} a^{2}=2$;
(3) $\sqrt{1-2 \sin 10^{\circ} \cos 10^{\circ}}=-a$.

Which of the following is correct?
(A) (1) and (2) are correct.
(B) (1) and (3) are correct.
(C) (2) and (3) are correct.
(D) All are correct.
(E) None are correct.
(Chinese Jilin Province Seven Cities and Prefectures Junior High School Mathematics Competition, 1985)
[Solution] Let $\sin 10^{\circ}-\cos 10^{\circ}=a$, then $a<0$.
Thus, (1) is obviously incorrect.
By $\log _{(-a)} a^{2}=\log _{(-a)}(-a)^{2}=2 \log _{(-a)}(-a)=2$, we know it is correct.
Also, $1-2 \sin 10^{\circ} \cos 10^{\circ}=\sin ^{2} 10^{\circ}+\cos ^{2} 10^{\circ}-2 \sin 10^{\circ} \cos 10^{\circ}$
$$
=\left(\sin 10^{\circ}-\cos 10^{\circ}\right)^{2} \text {, }
$$

then
$$
\sqrt{1-2 \sin 10^{\circ} \cos 10^{\circ}}=\left|\sin 10^{\circ}-\cos 10^{\circ}\right|=-a \text {. }
$$

In summary, (2) and (3) are correct.
Therefore, the answer is $(C)$.