13. (6 points) Starting from 12 o'clock, after $\qquad$ minutes, the hour hand and the minute hand form a $90^{\circ}$ angle for the first time; after 12 o'clock, the second time the hour hand and the minute hand form a $90^{\circ}$ angle is $\qquad$.
13. (6 points) Starting from 12 o'clock, after _ $16 \frac{4}{11}$ —minutes, the hour hand and the minute hand form a $90^{\circ}$ angle for the first time; after 12 o'clock, the hour hand and the minute hand form a $90^{\circ}$ angle for the second time at 12 o'clock $49 \frac{1}{11}$ minutes.
【Solution】Solution: The number of degrees the minute hand moves per minute is:
$$
360 \div 60=6 \text { (degrees), }
$$

The number of degrees the hour hand moves per minute is:
$$
6 \times 5 \div 60=0.5 \text { (degrees) }
$$

The time for the first right angle is:
$$
\begin{array}{l}
90 \div(6-0.5), \\
=90 \div 5.5, \\
=16 \frac{4}{11} \text { (minutes), }
\end{array}
$$

The time for the second right angle is:
$$
\begin{array}{l}
270 \div(6-0.5), \\
=270 \div 5.5, \\
=49 \frac{1}{11} \text { (minutes). }
\end{array}
$$

The time at this moment is:
12 o'clock $+49 \frac{1}{11}$ minutes $=12$ o'clock $49 \frac{1}{11}$ minutes.
Therefore, the answer is: $16 \frac{4}{11}, 12$ o'clock $49 \frac{1}{11}$ minutes.