Clocks

At 9:00 the hour-hand is at 270 $^\circ$ . Since the hour-hand moves 360 $^\circ$ in 12 hours, therefore it moves $\dfrac {360^\circ}{12\times 60} = \dfrac 12^\circ$ /min. Therefore by 9:38 minutes, it advances by $38 \times \dfrac 12 = 19^\circ$ to $270+19=289^\circ$ . At 9:38 the minute-hand is at $\dfrac {38}{60} \times 360^\circ = 228^\circ$ . The angle between the minute- and hour-hand at 9:38 is $289^\circ-228^\circ = 61^\circ = 61 \times 60 = \boxed{3660}$ minutes.