Question

Question 1: A frame {A} in 2D is rotated by 100°. (a) Determine the Rotation Matrix describing the configuration of the frame {A}. (b) Calculate the coordinates of a point P with respect to frame {A}, if it is at (10, 5) according the fixed reference frame at (0, 0). Question 2: A robot is moving in 2D, and its frame {A} is defined by a translation of (5, 6) and a rotation of 45°, with reference to the fixed reference frame {0} which is at the origin. (a) Find the Transformation Matrix ?T? or T?? (b) Find the Transformation Matrix ? T? or T?? (c) If the robot observes a landmark at (15, 12) in its own frame, calculate the coordinates of this landmark in the frame {0}. Question 3: A body frame b is defined a rotation matrix below: Rb = [ 0 -1 0 1 0 0 0 0 1 ] (a) Find the new rotation matrix by rotating the frame b by 90° with respect to its z-axis. (b) Find the new rotation matrix by rotating the frame b by 90° with respect to the z-axis of the fixed frame.

          Question 1:
A frame {A} in 2D is rotated by 100°.
(a) Determine the Rotation Matrix describing the configuration of the frame {A}.
(b) Calculate the coordinates of a point P with respect to frame {A}, if it is at (10, 5) according the fixed reference frame at (0, 0).

Question 2:
A robot is moving in 2D, and its frame {A} is defined by a translation of (5, 6) and a rotation of 45°, with reference to the fixed reference frame {0} which is at the origin.
(a) Find the Transformation Matrix ?T? or T??
(b) Find the Transformation Matrix ? T? or T??
(c) If the robot observes a landmark at (15, 12) in its own frame, calculate the coordinates of this landmark in the frame {0}.

Question 3:
A body frame b is defined a rotation matrix below:
Rb = [
0 -1 0
1  0 0
0  0 1
]
(a) Find the new rotation matrix by rotating the frame b by 90° with respect to its z-axis.
(b) Find the new rotation matrix by rotating the frame b by 90° with respect to the z-axis of the fixed frame.

Question 1:
A frame A in 2D is rotated by 100°.
(a) Determine the Rotation Matrix describing the configuration of the frame A.
(b) Calculate the coordinates of a point P with respect to frame A, if it is at (10, 5) according the fixed reference frame at (0, 0).

Question 2:
A robot is moving in 2D, and its frame A is defined by a translation of (5, 6) and a rotation of 45°, with reference to the fixed reference frame 0 which is at the origin.
(a) Find the Transformation Matrix ?T? or T??
(b) Find the Transformation Matrix ? T? or T??
(c) If the robot observes a landmark at (15, 12) in its own frame, calculate the coordinates of this landmark in the frame 0.

Question 3:
A body frame b is defined a rotation matrix below:
Rb = [
0 -1 0
1 0 0
0 0 1
]
(a) Find the new rotation matrix by rotating the frame b by 90° with respect to its z-axis.
(b) Find the new rotation matrix by rotating the frame b by 90° with respect to the z-axis of the fixed frame.

Added by Samantha M.

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