When your hand placement is correct and proper contact is achieved with PNF, the area being facilitated will experience increased…

You are using a PNF LE extremity pattern that includes the motions of hip extension, external rotation, adduction, and plantarflexion This corresponds to which of these PNF patterns?

According to Rood, all function is related to one of 2 biological purposes. Which of these correctly states one of those purposes?

Following treatment to address the problematic areas of gait, a patient may still be missing some of the elements of a natural gait pattern. Which of these treatment techniques would not address some of those missing elements?

You have a patient positioned in a pivot-prone posture. This treatment position can be used to facilitate the development of all of these except…

While working with a local athletic team one player complains of pain and is found to have pronounced weakness in the scapular retractors. Pt also has limited ROM of scapulae. Which technique below would be the most appropriate for this patient?

Five dialysis bags, constructed from a semipermeable membrane that is impermeable to sucrose, were filled with various concentrations of sucrose and then placed in separate beakers containing an initial concentration of 0.6 M sucrose solution. At 10-minute intervals, the bags were massed (weighed) and the percent change in mass of each bag was graphed. Which line in the graph represents the bag that was initially surrounded by the most hypertonic solution? 

Pre eclampsia is described by three characteristics except:

Problem 1. (15 pts) Consider the system depicted in the above block diagram, with the input \(u\) and output \(y\). Note that the three blocks marked with “\(s^{-1}\)” are the integrators (i.e., “\(\int\)”).  Identify a set of state variables and derive the state space model of the system. Problem 2. (30 pts) Let \(A=\begin{bmatrix}1& 2\\-3&-4\end{bmatrix}\). (a) (5 pts) Find the eigenvalues of \(A\).  (Hint: they are two integers.) (b) (10 pts) Express \(A^{100}\) as a proper linear combination of \(A\) and the identity matrix \(I\). (c) (10 pts) Use your favorite method to find the analytic expression of \(e^{At}\). (d) (5 pts) Write the solution \(x(t)\) starting from x(0)={“version”:”1.1″,”math”:”x(0)=”}1-1{“version”:”1.1″,”math”:”1-1″} as a linear combination of the modes. Problem 3. (24 pts) Consider the matrix defined below (\(T\) is nonsingular): A=v1v2v3v4⏟T{“version”:”1.1″,”math”:”A=v1v2v3v4⏟T”}-0.5-110-10⏟J{“version”:”1.1″,”math”:”-0.5-110-10⏟J”}w1Tw2Tw3Tw4T⏟T-1{“version”:”1.1″,”math”:”w1Tw2Tw3Tw4T⏟T-1″} First consider the continuous-time LTI system \(\dot x=Ax\). (a) (2 pts) Is the continuous-time system stable, marginally stable, or unstable? Explain why. (b) (4 pts) Find all the modes of the system \(\dot x=Ax\). (c) (6 pts) For each of the following properties, determine if there exists some \(x(0)\neq 0\) so that the resulting solution \(x(t)\) satisfies the property. If yes, find one such \(x(0) \); If no, explain why. (i) \(x(t)\to 0\) (ii) \(x(t)\) is unbounded (iii) \(x(t)\) is bounded and does not converge to \(0\) Next consider the discrete-time LTI system \(x[k+1]=Ax[k] \). (d) (2 pts) Is the discrete-time system stable, marginally stable, or unstable? Explain why. (e) (4 pts) Find all the modes of the system \(x[k+1]=Ax[k] \). (f) (6 pts) For each of the following properties, determine if there exists some \(x[0]\neq 0\) so that the resulting solution \(x[k]\) satisfies the property. If yes, find one such \(x[0] \); If no, explain why. (i) \(x[k]\to 0\) (ii) \(x[k]\) is unbounded (iii) \(x[k]\) is bounded and does not converge to \(0\) Problem 4. (15 pts) Find the fundamental matrix \(\Phi(t)\) of the LTV system \(\dot x(t) = \begin{bmatrix} -\frac{1}{t+2} & e^{t} \\ 0 & -1 \end{bmatrix} x(t)\). Problem 5. (16 pts) Consider a system \(\dot x=Ax\) with \(x\in\mathbb R^3\) and \(A\in\mathbb R^{3\times 3}\).  Suppose the system has a solution x(t)={“version”:”1.1″,”math”:”x(t)=”}e-t+11+te-t(1+t)e-t{“version”:”1.1″,”math”:”e-t+11+te-t(1+t)e-t”}. (a) (5 pts) Find the eigenvalues of \(A\) and their Jordan block sizes. (b) (5 pts) Write the given \(x(t)\) as a linear combination of the modes of the system. (c) (6 pts) Find \(A\) and \(x(0)\) that results in the solution \(x(t)\). Congratulations, you are almost done with Midterm Exam 1.  DO NOT end the Honorlock session until you have submitted your work to Gradescope.  When you have answered all questions:  Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible.  Submit your PDF to Gradescope as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.).  Click this link to go to Gradescope to submit your work: Midterm Exam 1 Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam.  End the Honorlock session. 

Lolly opens a coffee shop and applies to the U.S.P.T.O. for the trademark “Coffee.” Is she likely to be granted a trademark?