2. A vector xE2has a representation = with respect to the natural basis e, -(1)--01)...

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α₁ 2. A vector xE2has a representation α = with respect to the natural basis e, -(1)-₁₂-01) in Az the Cartesian coordinate system. A transformation Trotates the vector x counterclockwise by 90°. The coordinate system is also rotated counterclockwise by 45°. Find the representation B = of the - (B) rotated vector y = Tx in the coordinate system that results from the rotation of the original system. Express I in matrix form. tom ***** The transfer function of a system is H(s) = s² + s s³ +5s² +9s +5 It is desired to estimate as many states of the system as possible. Design an appropriate observer that has a response time no less than one-twentieth of the time constant of the system. ***** α₁ 2. A vector xE2has a representation α = with respect to the natural basis e, -(1)-₁₂-01) in Az the Cartesian coordinate system. A transformation Trotates the vector x counterclockwise by 90°. The coordinate system is also rotated counterclockwise by 45°. Find the representation B = of the - (B) rotated vector y = Tx in the coordinate system that results from the rotation of the original system. Express I in matrix form. tom ***** The transfer function of a system is H(s) = s² + s s³ +5s² +9s +5 It is desired to estimate as many states of the system as possible. Design an appropriate observer that has a response time no less than one-twentieth of the time constant of the system. *****

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