Answer to Problem 1.
You can take
and
.
Or you can take
and
.
![[Maple Math]](images/decomp7.gif)
and
![[Maple Math]](images/decomp8.gif)
.
and
.
![[Maple Math]](images/decomp9.gif)
and
![[Maple Math]](images/decomp10.gif)
.