Numerade

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Consider a SISO system state equation: $$ \mathbf{\dot{x}} = \underbrace{\begin{bmatrix} \eta & 1 & 0 & \dots & 0 \\ 0 & \eta & 1 & \dots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \dots & 1 \\ 0 & 0 & 0 & \dots & \eta \end{bmatrix}}_{\mathbf{A}} \mathbf{x} + \underbrace{\begin{bmatrix} b_1 \\ b_2 \\ \vdots \\ b_{n-1} \\ b_n \end{bmatrix}}_{\mathbf{B}} u $$ $$ y = \underbrace{\begin{bmatrix} c_1 & c_2 & \dots & c_{n-1} & c_n \end{bmatrix}}_{\mathbf{C}} \mathbf{x} $$ (a) Show that (A, B) is controllable if and only if $b_n \ne 0$. (5%) (b) Show that (A, C) is observable if and only if $c_1 \ne 0$. (5%)

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Question 14 (1 point) (*) A digital option is an option that always pays off $1 if the option expires in the money, and $0 otherwise. For example, in this question a digital call option with a strike price of $80 will pay only $1 rather than $20 when stock price goes to $100, and $0 otherwise. What should be the price for this digital call option today? Question 14 options: $0 $0.3 $0.7 $1

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Question 2 Data from multiple databases is often integrated into a single repository called a A Data Center B Data Element C Data Cube D Data Warehouse Last saved 10:20:38 AM 2 Points

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After your last camping trip, you decide to step up your conquests. You travel to Argentina and climb Aconcagua and want to test your knowledge of the relationship of atmospheric pressure to elevation. At what temperature do you have to heat your water to get it to boil, just the temperature in degrees Fahrenheit? - no units needed, just the value....

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All of the following are true of connection-oriented and connectionless protocols, except: a. Internet Protocol is called a connectionless protocol. b. A connection-oriented protocol sets up a connection between the source and destination, and all messages the two hosts exchange during the conversation use the same connection information. c. A connectionless protocol treats each message separately. d. A network cannot support both connectionless and connection-oriented protocols.

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Question 2 Answer the following parts about the fundamental parameters of antennas and radiation mechanisms: The formula of the electric field of finite length dipole is: $$E_\theta = \frac{jI_0 l e^{-jkr}}{2\pi r} \left| \frac{\cos \left(\frac{kl}{2}\cos\theta\right) - \cos \left(\frac{kl}{2}\right)}{\sin \theta} \right| $$ Write the electric filed formulas of $\lambda/2$ (i.e. $l = \lambda/2$) dipole and for a dipole (i.e. $l = \lambda$). If we are 0.8$\lambda$ away from both antenna, which antenna is in far field region? Justify your answer.

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Calculate the molar solubility of ZnS ($K_{sp} = 2.0 \times 10^{-11}$) in 0.411 M $Na_2S$ at 25 degrees C. Report your answer to two significant figures and do NOT include units. Express your answer using "e" for scientific notation. For example, $1.0 \times 10^{-14}$ is 1.0e-14.

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Br ce C-C-C-C-C | ce ce C-C-C-C-C ce Br CH3 C C C-C-C-C-C C C C C CH3 CH3 C=C C C Ce BrF

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Central Mass Ambulance Service can purchase a new ambulance for $200,000 that will provide an annual net cash flow of $100,000 per year for two years. The salvage value of the ambulance will be $25,000. Assume the ambulance is sold at the end of year 2. Calculate the NPV of the ambulance if the required rate of return is 9%. (Round your answer to the nearest $1.) ? ?. $24,089 B. -$3,047 C. $3,047 D. -$24,089

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Question 1 a) Determine the final value of $X(z) = \frac{1}{1 - z^{-1}} - \frac{1}{1 - e^{-aT}z^{-1}}$, $a > 0$ by using the Final Value Theorem [7 marks] b) Find the Nyquist rate for the following analogue signal $x(t) = 3 \cos(50\pi t) + 10 \sin(300\pi t) - \cos(100\pi t)$ [8 marks] c) A continuous time PD controller can be discretized as follows: $u(t) = K_p e(t) + K_d \frac{de(t)}{dt} \implies u(kT) = K_p e(kT) + K_d \left[\frac{e(kT) - e((k-1)T)}{T}\right]$ where k represents the discrete time instants and T is the sampling period. State the condition T, $K_p$ and $K_d$ should satisfy for this controller to be stable. [10 marks]

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latoya b.