coordinate transformation and scaling

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I have a global coordinate system that I need to transform to a local coordinate system. The new and old coordinate systems are shown below.

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Using transformation rules, I came with with the coordinates in the new system. To get the coordinate system in the right position, it has to translated in the x and y directions, rotated about the x and z axis, and scaled. These formulas are shown below.

enter image description here

These formulas are not working, and I'm not sure why? As test points I tried out these,

Old System (0,-1.11270165)

New System (5.88729835,-10)

If anyone can enlighten me it would be greatly appreciated. Thanks.