


'''simple docstring'''
from __future__ import annotations


def       _lowercase							(					UpperCamelCase__							:       int = 4      ):
 __A	:		Any	  =      abs(_snake_case      ) or 4
 return [[1 + x + y * row_size for x in range(_snake_case      )] for y in range(_snake_case      )]


def       _lowercase							(					UpperCamelCase__							:       list[list[int]]      ):
 return reverse_row(transpose(_snake_case      )      )
 # OR.. transpose(reverse_column(matrix))


def       _lowercase							(					UpperCamelCase__							:       list[list[int]]      ):
 return reverse_row(reverse_column(_snake_case      )      )
 # OR.. reverse_column(reverse_row(matrix))


def       _lowercase							(					UpperCamelCase__							:       list[list[int]]      ):
 return reverse_column(transpose(_snake_case      )      )
 # OR.. transpose(reverse_row(matrix))


def       _lowercase							(					UpperCamelCase__							:       list[list[int]]      ):
 __A	:		Optional[Any]	  =      [list(_snake_case      ) for x in zip(*_snake_case      )]
 return matrix


def       _lowercase							(					UpperCamelCase__							:       list[list[int]]      ):
 __A	:		Optional[int]	  =      matrix[::-1]
 return matrix


def       _lowercase							(					UpperCamelCase__							:       list[list[int]]      ):
 __A	:		Optional[Any]	  =      [x[::-1] for x in matrix]
 return matrix


def       _lowercase							(					UpperCamelCase__							:       list[list[int]]      ):


 for i in matrix:
  print(*_snake_case      )


if __name__ == "__main__":
 UpperCAmelCase_			:  Any										=   make_matrix()
 print('\norigin:\n')
 print_matrix(matrix)
 print('\nrotate 90 counterclockwise:\n')
 print_matrix(rotate_aa(matrix))

 UpperCAmelCase_			:  Any										=   make_matrix()
 print('\norigin:\n')
 print_matrix(matrix)
 print('\nrotate 180:\n')
 print_matrix(rotate_aaa(matrix))

 UpperCAmelCase_			:  int										=   make_matrix()
 print('\norigin:\n')
 print_matrix(matrix)
 print('\nrotate 270 counterclockwise:\n')
 print_matrix(rotate_aaa(matrix))












"""simple docstring"""

import math






def 		_snake_case	(   _snake_case				:   float							,    _snake_case				:   float				)       ->   float:






      '''simple docstring'''


      if (
          not isinstance(_snake_case							,    (int, float)				)
          or power_factor < -1
          or power_factor > 1
      ):
            raise ValueError('power_factor must be a valid float value between -1 and 1.'				)
      return apparent_power * power_factor






def 		_snake_case	(   _snake_case				:   float							,    _snake_case				:   float				)       ->   float:






      '''simple docstring'''


      if (
          not isinstance(_snake_case							,    (int, float)				)
          or power_factor < -1
          or power_factor > 1
      ):
            raise ValueError('power_factor must be a valid float value between -1 and 1.'				)
      return apparent_power * math.sqrt(1 - power_factor**2				)


if __name__ == "__main__":
       import doctest

       doctest.testmod()

