Numerade

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2.6 Matrix Transformations 1. b. Write $\mathbf{a} = \begin{bmatrix} 3 \\ 2 \\ -1 \end{bmatrix}$, $\mathbf{b} = \begin{bmatrix} 2 \\ 0 \\ 5 \end{bmatrix}$ and $\mathbf{x} = \begin{bmatrix} 5 \\ 6 \\ -13 \end{bmatrix}$. We are given $T(\mathbf{a})$ and $T(\mathbf{b})$, and are asked to find $T(\mathbf{x})$. Since $T$ is linear it is enough (by Theorem 2.6.1) to express $\mathbf{x}$ as a linear combination of $\mathbf{a}$ and $\mathbf{b}$. If we set $\mathbf{x} = r\mathbf{a} + s\mathbf{b}$, equating entries gives equations $3r + 2s = 5$, $2r = 6$ and $-r + 5s = -13$. The (unique) solution is $r = 3$, $s = -2$, so $\mathbf{x} = 3\mathbf{a} - 2\mathbf{b}$. Since $T$ is linear we have $T(\mathbf{x}) = 3T(\mathbf{a}) - 2T(\mathbf{b}) = 3\begin{bmatrix} 3 \\ 5 \end{bmatrix} - 2\begin{bmatrix} -1 \\ 2 \end{bmatrix} = \begin{bmatrix} 11 \\ 11 \end{bmatrix}$

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You are always hungry at the end of the school day, so you walk home on the route that takes you past a food truck so you can buy a taco. Which explanation for your behavior would be given using drive theory? Group of answer choices You have a need for food, which spurs a hunger drive that motivates you to satisfy the drive. You have an instinct that leads you to locations where food is abundant. You are rewarded for walking in the direction of the food truck with the acquisition of a tasty taco. The walk to the food trucks keeps you in a state of optimum physiological arousal.

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(Matching) Which names match which experiments. Hershey Watson Macloid Meselson McCarty Stahl Crick Franklin 1. Eliminated protein, polysaccharides, lipids, and RNA as the genetic material. 2. G=C; A=T 3. structure of DNA 4. DNA missing in phage ghosts 5. semiconservative replication 6. transformation

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Which of the following is not an example of kinetic energy? Diving off of the diving board at Rapids on the Reservoir Primtime running up the field with the team Water held behind a dam

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This figure shows a phylogeny of the Bromeliad Family of plants and the regions in which the species in this family are located. 1) True or False: Based on this phylogeny, the Pitcairnioideae are more closely related to the Puyoideae than to the Bromelioideae. Questions 36-37] This figure shows a phylogeny of the Bromeliad Family of plants and the regions in which the species in this family are located. (Givnish et al. 2011, American Journal of Botany 98(5): 872-895) Bromelioideae Pitcairnioideae Puyoideae Historical Biogeography MP/BI/S-DIVA Guayana Shield l Brazilian Shield Amazonia Andes, S Chile N South America Caribbean SE USA I Central America West Aric - Navioides Hechtioideae Tillandsioideae Jndmer

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Bob wants to send Alice the message, "JAW," which he plans to encrypt using Alice's RSA cypher with public key (pq, e) = (55, 3). To encrypt the message, Bob uses the method described in Example 8.4.9. He encodes one letter at a time using A = 01, B = 02, C = 03, , Z = 26. Next, he applies the encrypting formula C = Me mod pq,

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Before the deployment of the Iraqi Freedom military operation in March 2003, a sample of 510 telephone interviews was conducted by the Washington Post-ABC Poll to gauge the approval or disapproval of the war. In sum, 326 out of 510 of those polled approved of how the president handled the Iraqi situation. In October 2002, the same poll showed that the approval rating was 291 out of 510. We want to test whether the proportion who approved the war decreased.\ Population 1 is defined as October 2003, and Population 2 is March 2003.\ The alternative hypothesis test (Ha) is [Select] [Select] , and the pooled proportion is

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2. A water jet with uniform velocity $V_1 = 5 \text{ m/s}$ and area $A_1 = 5 \text{ m}^2$ impinges on the object shown in Figure 1. The jet is deflected as in Figure 1 with angle $30^\circ$ with respect to the horizontal. The exit cross sectional area is $A_2 = A_1/2$ and the exit uniform velocity is $V_2$. Density is $\rho = 1000 \text{ kg/m}^3$. Assuming steady, incompressible flow, find: a. The exit velocity $V_2$? [10 points] b. The horizontal force on the object. [20 pts] c. The vertical force on the object. [20 pts] You must clearly draw the control volume. All your calculations must be consistent with the control volume.

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In the following system, what is the Phase angle at the frequency $\omega=100\text{rad/s}$. \(G(s) = \frac{3(s + 5)}{s^2 (s + 1)(s + 2)}\ Select one: a. - 271.1° b. - 134.3° c. - 19.1° d. - 226.4°

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The interaction between two atoms is sometimes described by the so-called Morse potential: $V(r) = D_e[e^{-2\alpha(r-r_0)} - 2e^{-\alpha(r-r_0)}]$. (a) For this potential, verify that $D_e$ corresponds to the depth of the potential and $r_0$ corresponds to the bond length. (b) Letting the masses of the two atoms be $m_1$ and $m_2$, derive the ground vibrational frequency, $\nu = \omega/2\pi$, under the harmonic oscillator approximation around the bond length. (c) For the molecule HCl, $r_0 = 1.27 \AA$, $D_e = 4.62 \text{ eV}$, and $\alpha r_0 = 2.38$. Calculate its vibrational frequency $\nu$ and its dissociation energy $D_0$.

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jesse s.