⑴RTΔABC中,∠A=30°,∴∠B=60°,BC=1/2AB=8㎝,
∵BC=B1C,∴ΔBCB1是等边三角形,
∴BB1=BC=8㎝,
∴AB1=AB-BB1=8㎝.
⑵在ΔCAA1中,CA=CA1,
∴∠CA1A=∠A=30°,又∠CA1B1=30°,
∵∠ABC=∠AA1C+∠BCA1,∴60°=30°+∠BCA1,∠BCA1=30°,
∴∠BCB1=120°,又BC=B1C,∴∠CBB1=1/2(180°-∠BCB1)=30°,
∴∠ABB1=90°,AA1⊥BB1.
⑶ΔA1EA是等腰三角形,分三种情况：
①EA=EA1,则∠EA1A=∠EAA1,
∵CA=CA1,∴∠CA1A=∠CAA1,∴E、C重合,不合题意,舍去(C、E不可能重合).
②AA1=AE,∠A1AC=1/2(180°-α),
∴∠AA1E=∠AEA1=1/2［180°-1/2(180°-α)］=45°+1/4α,
又∠AA1E=∠AA1C-∠CA1B1=1/2(180°-α)-30°=60°-1/2α,
∴45°+1/4α=60°-1/2α,α=20°,
③A1A=A1E,
则ΔA1AE∽ΔCAA1,
∠AA1E=α,∠A1EA=1/2(180°-α)=90°-1/2α,
又∠A1EA=∠A1CA+∠CA1B1=α+30°,
∴90°-1/2α=α+30°,α=40°.
综上所述,旋转角α=20°或40°.