7. Starting from 12 o'clock, at least $\qquad$ minutes must pass for the hour hand and the minute hand to form equal angles with their positions at 12 o'clock (as shown in the figure where $\angle 1=\angle 2$ ).
【Solution】Solution: Let the time taken be $x$ hours.
$$
\begin{aligned}
30 x & =360-360 x \\
3 x+360 x & =360-30 x+360 \\
390 x & =360 \\
x & =\frac{12}{13} \\
\frac{12}{13} \text { hours } & =55 \frac{5}{13} \text { minutes. }
\end{aligned}
$$

Therefore, the answer is: $55 \frac{5}{13}$.