（本题满分 12 分）

已知二次型

\(f(x_{1},x_{2},x_{3})=x_{1}^{2}+2x_{2}^{2}+2x_{3}^{2}+2x_{1}x_{2}-2x_{1}x_{3}\)；

\(g(y_{1},y_{2},y_{3})=y_{1}^{2}+y_{2}^{2}+y_{3}^{2}+2y_{2}y_{3}\). 

（1）求可逆变换\(x = Py\)将\(f(x_{1},x_{2},x_{3})\)化成\(g(y_{1},y_{2},y_{3})\)

（2）是否存在正交变换\(x = Qy\)将\(f(x_{1},x_{2},x_{3})\)化成\(g(y_{1},y_{2},y_{3})\)