



"""simple docstring"""




from __future__ import annotations


def 	lowercase__  (      _UpperCAmelCase					)  ->      Dict:






      '''simple docstring'''


      if len(_a					) == 0:
            raise ValueError('find_min() arg is an empty sequence'					)
      lowercase	:   Union[str, Any]											= nums[0]
      for num in nums:
            lowercase	:   Optional[int]											= min(_a						,   _a					)
      return min_num


if __name__ == "__main__":
     import doctest

     doctest.testmod(verbose=True)





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) = }")
