






'''simple docstring'''







from math import cos, sin






def  lowerCAmelCase__		(					a_  :     float			)   -> Any:
       UpperCAmelCase__	:   str												=	float(_a			)
       return [[scaling_factor * int(x == y			) for x in range(2			)] for y in range(2			)]






def  lowerCAmelCase__		(					a_  :     float			)   -> Optional[int]:
       UpperCAmelCase__	:   List[str]												=	cos(_a			), sin(_a			)
       return [[c, -s], [s, c]]






def  lowerCAmelCase__		(					a_  :     float			)   -> Dict:
       UpperCAmelCase__	:   Optional[Any]												=	cos(_a			), sin(_a			)
       UpperCAmelCase__	:   Dict												=	c * s
       return [[c * c, cs], [cs, s * s]]






def  lowerCAmelCase__		(					a_  :     float			)   -> List[str]:
       UpperCAmelCase__	:   List[Any]												=	cos(_a			), sin(_a			)
       UpperCAmelCase__	:   Optional[Any]												=	c * s
       return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(f'    {scaling(5) = }')
print(f'  {rotation(45) = }')
print(f'{projection(45) = }')



print(f'{reflection(45) = }')




from math import cos, sin







def       lowerCamelCase_  (    _a       :						float    ):



    '''simple docstring'''




    UpperCAmelCase_     :       str  		=					float(_a    )
    return [[scaling_factor * int(x == y    ) for x in range(2    )] for y in range(2    )]







def       lowerCamelCase_  (    _a       :						float    ):



    '''simple docstring'''




    UpperCAmelCase_		, UpperCAmelCase_     :       List[str]  		=					cos(_a    ), sin(_a    )
    return [[c, -s], [s, c]]







def       lowerCamelCase_  (    _a       :						float    ):



    '''simple docstring'''




    UpperCAmelCase_		, UpperCAmelCase_     :       Optional[Any]  		=					cos(_a    ), sin(_a    )
    UpperCAmelCase_     :       Dict  		=					c * s
    return [[c * c, cs], [cs, s * s]]







def       lowerCamelCase_  (    _a       :						float    ):



    '''simple docstring'''




    UpperCAmelCase_		, UpperCAmelCase_     :       List[Any]  		=					cos(_a    ), sin(_a    )
    UpperCAmelCase_     :       Optional[Any]  		=					c * s
    return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(F"    {scaling(5) = }")
print(F"  {rotation(45) = }")
print(F"{projection(45) = }")






print(F"{reflection(45) = }")
