(a) Find the charge, baryon number, strangeness, charm, and bottomness of the $J / \Psi$ particle from its quark composition. (b) Do the same for the $\Upsilon$ particle.

Determine whether the vector v is a linear combination of the vectors $\mathbf{v}_{1}, \mathbf{v}_{2}$, and $\mathbf{v}_{3}$.

$$\mathbf{v}=\left[\begin{array}{l} 6 \\ 3 \\ 3 \\ 7 \end{array}\right] \quad \mathbf{v}_{1}=\left[\begin{array}{l} 2 \\ 3 \\ 4 \\ 5 \end{array}\right]$$

$$\mathbf{v}_{2}=\left[\begin{array}{r} 1 \\ -1 \\ 2 \\ 3 \end{array}\right] \quad \mathbf{v}_{3}=\left[\begin{array}{r} 3 \\ 1 \\ -3 \\ 1 \end{array}\right]$$

Sketch the graph of the function. Identify the vertical asymptote.

$$y=\log _{4}(x-2)+3$$

Determine the method of solving the quadratic equation that would be most convenient. Explain your reasoning. 2x$^{2}$ - 9x + 12 = 0

Write the equation of the parabola in standard form, and find the vertex of its graph. y = x$^{2}$ - 8x + 3

One decay mode for the eta-zero meson is $\eta^{0} \rightarrow \pi^{0}+\pi^{0}.$ (a) Write the decay in terms of the quark constituents. (b) How much energy is released? (c) What is the ultimate release of energy, given the decay mode for the pi zero is $\pi^{0} \rightarrow \gamma+\gamma ?$

What is the oxidation state of the halogen in each of the following? (a) $\mathrm{H}_{5} \mathrm{IO}_{6}$ (b) $\mathrm{IO}_{4}^−$ (c) $\mathrm{ClO}_{2}$ (d) $\mathrm{ICl}_{3}$ (e) $\mathrm{F}_{2}$

A section of superconducting wire carries a current of 100 A and requires 1.00 L of liquid nitrogen per hour to keep it below its critical temperature. For it to be economically advantageous to use a superconducting wire, the cost of cooling the wire must be less than the cost of energy lost to heat in the wire. Assume that the cost of liquid nitrogen is $0.30 per liter, and that electric energy costs$0.10 per $kW\cdot h.$ What is the resistance of a normal wire that costs as much in wasted electric energy as the cost of liquid nitrogen for the superconductor?

Name three different methods of finding the closed-loop frequency response from the open-loop transfer function.

(a) What is the uncertainty in the energy released in the decay of a $\pi^{0}$ due to its short lifetime? (b) What fraction of the decay energy is this, noting that the decay mode is $\pi^{0} \rightarrow \gamma+\gamma$ (so that all the $\pi^{0}$ mass is destroyed)?

If a pole is moved with a constant imaginary part, what will the responses have in common?

For the following response functions, determine if pole-zero cancellation can be approximated. If it can, find percent overshoot, settling time, rise time, and peak time.

$$\text { a. } C(s)=\frac{(s+4)}{s(s+2)\left(s^{2}+3 s+10\right)}$$

$$\text { b. } C(s)=\frac{(s+2.5)}{s(s+2)\left(s^{2}+4 s+20\right)}$$

$$\text { c. } C(s)=\frac{(s+2.2)}{s(s+2)\left(s^{2}+s+5\right)}$$

$$\text { d. } C(s)=\frac{(s+2.01)}{s(s+2)\left(s^{2}+5 s+20\right)}$$

Predict and explain the regiochemical outcome for chlorination of bromobenzene.

Use a definition of the derivative to find the rate of change of f at the indicated numbers. $f(x)=\sqrt{x}$ at (a) c=1, (b) c=4, (C) c any positive real number