题目

It was Monday. Mrs. Smith's dog was hungry, but there was not any meat in the house. Considering that there was no better way. Mrs. Smith took a piece of paper, and wrote the following words on it: “Give my dog half a pound of meat.” Then she gave the paper to her dog and said gently: “Take this to the butcher(屠夫). And he's going to give you your lunch today.” Holding the piece of paper in its mouth, the dog ran to the butcher's. It gave the paper to the butcher. The butcher read it carefully, recognized that it was really the lady's handwriting and soon did it as he was ask如图，平行四边形ABCD中，AB⊥AC，AB=1，BC= ．对角线AC，BD相交于点O，将直线AC绕点O顺时针旋转，分别交BC，AD于点E，F． （1）证明：当旋转角为90°时，四边形ABEF是平行四边形；（2）试说明在旋转过程中，线段AF与EC总保持相等；（3）在旋转过程中，四边形BEDF可能是菱形吗？如果不能，请说明理由；如果能，说明理由并求出此时AC绕点O顺时针旋转的度数．