Q&A

(noun)

A period of time in which questions are asked of a person.

Examples of Q&A in the following topics:

  • Reaction Quotients

    • The reaction quotient is a measure of the relative amounts of reactants and products during a chemical reaction at a given point in time.
    • The reaction quotient, Q, is a measure of the relative amounts of reactants and products during a chemical reaction at a given point in time.
    • This expression shows that Q will eventually become equal to Keq, given an infinite amount of time.
    • The ball in the initial state is indicative a reaction in which Q < K; in order to reach equilibrium conditions, the reaction proceeds forward.
    • Calculate the reaction quotient, Q, and use it to predict whether a reaction will proceed in the forward or reverse direction
  • Electric Potential Due to a Point Charge

    • The electric potential of a point charge Q is given by $V=\frac{kQ}{r}$.
    • Another way of saying this is that because PE is dependent on q, the q in the above equation will cancel out, so V is not dependent on q.
    • The electric potential due to a point charge is, thus, a case we need to consider.
    • Using calculus to find the work needed to move a test charge q from a large distance away to a distance of r from a point charge Q, and noting the connection between work and potential (W=–qΔV), it can be shown that the electric potential V of a point charge is
    • The electric potential is a scalar while the electric field is a vector.
  • Exercises

    • For the following data, plot the theoretically expected z score as a function of the actual z score (a Q-Q plot).
    • For the data in problem 2, describe how the data differ from a normal distribution.
    • For the "SAT and College GPA" case study data, create a contour plot looking at College GPA as a function of Math SAT and High School GPA.
    • Naturally, you should use a computer to do this.
    • Naturally, you should use a computer to do this.
  • Quantile-Quantile (q-q) Plots

    • Describe the shape of a q-q plot when the distributional assumption is met.
    • Here we define the qth quantile of a batch of n numbers as a number ξqsuch that a fraction q x n of the sample is less than ξq, while a fraction (1 - q) x n of the sample is greater than ξq.
    • As before, a normal q-q plot can indicate departures from normality.
    • (Right) q-q plot of a sample of 100 uniform points
    • Figure 6. q-q plots of a sample of 10 and 1000 uniform points
  • B.3 Chapter 3

    • A particle of mass $m$, charge $q$, moves in a plane perpendicular to a uniform, static, magnetic field $B$.
    • If at time $t=0$ the particle has a total energy $\displaystyle t = \frac{ r_i^3 m^2 c^3}{4 e^4 } = \frac{1}{4 c} r_i \left ( \frac{r_i}{r_0} \right )^2$, show that it will have energy $E=\gamma m c^2 < E_0$ at a time ${\bf F} = -\hat{\bf r} \frac{q^2}{r^2}$, where$t \approx \frac{3 m^3 c^5}{2 q^4 B^2} \left ( \frac{1}{\gamma} - \frac{1}{\gamma_0} \right ).$
    • A particle of mass $m$ and charge $q$ moves in a circle due to a force ${\bf F} = -\hat{\bf r} \frac{q^2}{r^2}$.
    • What is the time if $\displaystyle P = \frac{2 q^2 \dot{u}^2}{3 c^3} = \frac{2 q^2 }{3 c^3} \left ( \frac{q^2}{r^2 m} \right )^2$ A (for an hydrogen)?
    • There is a natural limit to the luminosity a gravitationally bound object can emit.
  • Costs and Production in the Short-Run

    • Average Fixed Cost (AFC) is the FC divided by the output or TP, Q, (remember Q=TP).
    • AFC is fixed cost per Q.
    • It is the variable cost per Q.
    • AC = TC/Q.
    • Marginal cost (MC) is the change in TC or VC "caused" by a change in Q (or TP).
  • The Linear Algebra of the DFT

    • Define a matrix $Q$ such that
    • The matrix appearing in Equation 4.6.3 is the complex conjugate of $Q$ ; i.e., $Q^*$ .
    • The matrix $Q$ is almost orthogonal.
    • We have said that a matrix $A$ is orthogonal if $A A^T = A^T A = I$, where $I$ is the N-dimensional identity matrix.
    • Once again, orthogonality saves us from having to solve a linear system of equations: since $Q^* = Q^{-1}$ , we have
  • Solving Problems with Vectors and Coulomb's Law

    • To address the electrostatic forces among electrically charged particles, first consider two particles with electric charges q and Q , separated in empty space by a distance r.
    • (The electric force vector has both a magnitude and a direction. ) We can express the location of charge q as rq, and the location of charge Q as rQ.
    • Electric Force on a Field Charge Due to Fixed Source Charges
    • Suppose there is more than one point source charges providing forces on a field charge. diagrams a fairly simple example with three source charges (shown in green and indexed by subscripts) and one field charge (in red, designated q).
    • In a simple example, the vector notation of Coulomb's Law can be used when there are two point charges and only one of which is a source charge.
  • Profit Maximization Function for Monopolies

    • In this formula, p(q) is the price level at quantity q.
    • The cost to the firm at quantity q is equal to c(q).
    • As a result, the first-order condition for maximizing profits at quantity q is represented by:
    • Consider the example of a monopoly firm that can produce widgets at a cost given by the following function:
    • This occurs because marginal revenue is the demand, p(q), plus a negative number.
  • Some Special Matrices

    • As an exercise, show that $A I_n = I_n A = A$ for any $n\times x$ matrix $A$ .
    • A matrix $Q \in \mathbf{R}^{{n \times n}}$ is said to be orthogonal if $Q^TQ = I_n$ .
    • In this case, each column of $Q$$\mathbf{q}_i \cdot \mathbf{q}_i = 1$ is an orthonormal vector: $\mathbf{q}_i \cdot \mathbf{q}_i = 1$ .
    • Now convince yourself that $Q^TQ = I_n$ implies that $QQ^T = I_n$ as well.
    • In which case the rows of $Q$ must be orthonormal vectors too.
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