


from math import cos, sin

def  lowerCAmelCase__				(    a__:	Dict )						->	Tuple:


							'''simple docstring'''





							_UpperCAmelCase					=    float(a__ )
							return [[scaling_factor * int(x == y ) for x in range(2 )] for y in range(2 )]

def  lowerCAmelCase__				(    a__:	Tuple )						->	Optional[int]:


							'''simple docstring'''





							_UpperCAmelCase	, _UpperCAmelCase					=    cos(a__ ), sin(a__ )
							return [[c, -s], [s, c]]

def  lowerCAmelCase__				(    a__:	Optional[int] )						->	Optional[Any]:


							'''simple docstring'''





							_UpperCAmelCase	, _UpperCAmelCase					=    cos(a__ ), sin(a__ )
							_UpperCAmelCase					=    c * s
							return [[c * c, cs], [cs, s * s]]

def  lowerCAmelCase__				(    a__:	Union[str, Any] )						->	List[str]:


							'''simple docstring'''





							_UpperCAmelCase	, _UpperCAmelCase					=    cos(a__ ), sin(a__ )
							_UpperCAmelCase					=    c * s
							return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(f'''    {scaling(5) = }''')
print(f'''  {rotation(4_5) = }''')
print(f'''{projection(4_5) = }''')







print(f'''{reflection(4_5) = }''')




from __future__ import annotations

def  lowerCAmelCase__				(    a__:	list[int]    ,						a__:	int )						->	list[int]:


							'''simple docstring'''





							_UpperCAmelCase					=    {}
							for index, val in enumerate(a__ ):
														_UpperCAmelCase					=    target - val
														if compl in chk_map:
																					return [chk_map[compl], index]
														_UpperCAmelCase					=    index
							return []


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		print(f'''{two_sum([2, 7, 1_1, 1_5], 9) = }''')
