Numerade

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7. Consider the following vectors in $\mathbb{R}^3$. Determine the if there exists a non-zero real number $t$ and a real number $s$ such that $v_1 = tv_2 + sv_3$. $v_1 = \begin{pmatrix} 1 \\ 2 \\ 6 \end{pmatrix}, v_2 = \begin{pmatrix} 6 \\ 11 \\ 2 \end{pmatrix}, v_3 \begin{pmatrix} 0 \\ 4 \\ 7 \end{pmatrix}$ 8. Does the set of vectors $\{v_1, v_2, v_3\}$ as above span $\mathbb{R}^3$? Explain. 9. Determine if a given set of vectors forms a basis for a vector space

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Recall that a maximum distance separable (MDS) code is one that achieves the Singleton bound d=n-k+1. Let C be a linear (n,k,d)_(q) code over F_(q). (a) Prove that C is MDS if and only if every set of k coordinate positions has the following property: Every ordered k-tuple (x_(1),x_(2),dots,x_(k)) with x_(i)inF_(q) for i=1,.....,k, appears in the k coordinate positions in exactly one codeword. (b) Show that C is MDS if and only if its dual code is MDS. (Here, we assume that k < n.) Recall that a maximum distance separable (MDS) code is one that achieves the Singleton bound d = n -- k + 1. Let C be a linear (n, k, d)q code over Fq (a) Prove that C is MDS if and only if every set of k coordinate positions has the following property: Every ordered k-tuple (1,2,...,k) with x; e Fq for i = 1,...,k, appears in the k coordinate positions in exactly one codeword. (b) Show that C is MDS if and only if its dual code is MDS. (Here, we assume that k < n.)

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The block diagram shown in Figure 1 represents an unmanned car's speed function. Accelerator/Braker Desired Speed + $G_c(s)$ Speed Dynamics Actual Speed $G_u(s)$ Figure 1: Unmanned car's speed control system. \frac{K(s+8)}{(s+3)(s+6)(s+10)} Design a PD The transfer function of speed dynamics has been derived as, $G_u(s) = $ controller so that the system can operate with an ID+1 fold reduction in peak time at 20% overshoot. [ID value will be the last digit of your ID. Example: If your ID is 21-12345-1, ID = 1.] [Hints: $T_p = \frac{\pi}{\omega_n\sqrt{1-\zeta^2}}$, $T_s = \frac{4}{\zeta\omega_n}$, $%O.S = e^{\frac{-\pi\zeta}{\sqrt{1-\zeta^2}}}\times100$; $\zeta = \frac{|ln(\frac{%O.S}{100})|}{\sqrt{[ln(\frac{%O.S}{100})]^2+\pi^2}}$] Requirements: 1. Sketch the root locus of the uncompensated and compensated system. 2. Determine the old and new dominant pole of the system at an overshoot of 20% [use a suitable simulation tool]. 3. Compare the step response of compensated and uncompensated system using appropriate simulation tools (i.e. MATLAB).

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Nixtamalization is a traditional way of processing corn that results in which of the following nutritional benefits? Check all that apply: A. Reduced toxins B. Increased iron and calcium content C. Increased dietary fiber availability D. Ability of the body to access the Vitamin B3, or niacin, present in corn

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Express the function $F$ in the form $f \circ g$. $F(x) = \sqrt{x} + 2$ $(f(x), g(x)) = ($\qquad$)

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1. Compute the angle of twist of the free end relative to the fixed end of the steel bar shown in Figure 1. Assume $G_{steel} = 80 \text{ GPa}$. 1200 mm 400 mm Torque = 200 N·m Fixed surface 40 mm dia. 20 mm dia. Figure 1: Step-Down Shaft Torqued at its Free End.

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Problem 3. The elliptic curve modulo p, denoted by Ep, is the set of solutions (x, y) satisfying y² ? x³ + ax² + bx + c (mod p). Find all solutions to the following elliptic curve. How many solutions points are there? E?: y² ? x³ + 1 (mod 5)

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Why is the relation, represented by the arrow diagram below, NOT a function?

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If an object measures 2 cm and the image measures 3 cm, what would be the percent magnification of the object?

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4. A piston cylinder arrangement contains 3kg of R134a, initially at 1000kPa and 60°C. The refrigerant is condensed in a constant pressure process such that the cylinder finally has a 90% vapor by mass. Determine a) the final temperature, b) work done, and c) heat transfer during the process.

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cristina r.