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【简答题】
如图,以等边△OAB的边OB所在直线为x轴,点O为坐标原点,使点A在第一象限建立平面直角坐标系,其中△OAB边长为6个单位,点P从O点出发沿折线OAB向B点以3单位/秒的速度向B点运动,点Q从O点出发以2单位/秒的速度沿折线OBA向A点运动,两点同时出发,运动时间为t(单位:秒),当两点相遇停止。 (1)点A坐标为_____________,P、Q两点相遇时交点的坐标为________________; (2)当t=2时, ____________;当t=3时, ____________; (3)设△OPQ的面积为S,试求S关于t的函数关系式; (4)当△OPQ的面积最大时,试求在y轴上能否找一点M,使得以M、P、Q为顶点的三角形是Rt△,若能找到请求出M点的坐标,若不能找到请简单说明理由。
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