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Calculate the [H3O+]of each aqueous solution with the following [OH−]. NaOH, 1.0 x 10-2

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Which of the following statements regarding diffusion is FALSE? Group of answer choices Oxygen can simply diffuse across a plasma membrane in the direction from higher O2 concentration to lower O2 concentration. The concentration gradient is eliminated when a substance reaches equal concentrations (not volumes) on either side of a membrane. When a substance reaches equilibrium, no atoms or molecules of the substances will move across the membrane. Increasing the temperature will increase diffusion of substances. Both the chemical concentration gradient and an electrical or charge gradient can affect the diffusion of charged substances, such as ions. Na+ ions can diffuse through a plasma membranes' channel proteins (i.e., via facilitated diffusion), and when they do this, they will move from the area of high Na+ concentration to the area of lower Na+ concentration.

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Your company purchased K new 3D printers that are ready for testing. Each machine (3D printer) $M_i$, has a known probability of printing a defective product: $p_i$, $i = 1, 2, \dots, K$. The initial test consists of operating one 3D printer selected at random, and testing its first printed product. a) What is the probability that the first printed product is defective? b) If the first printed product is defective, what is the probability that it was printed by machine $M_i$? c) If the first printed product is found defective, the next step is to have the same machine print a second product for testing. What is the probability that the second printed product is also defective?

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3. Examine the following transformations, and assign oxidation states to any carbon atoms that undergo changes in bonding. Then, indicate whether each is a net oxidation or a net reduction or if no net redox reaction has occurred with respect to the organic substrate. If a redox reaction did occur, indicate how many electrons have been transferred. a. OH CH$_3$ Cl CH$_3$ Cl b. OCH$_3$ + 2 CH$_3$OH H$_3$CO OH c. OH d. Ph + CH$_3$Li Ph CH$_3$ e. H$_3$C N CH$_3$ H$_3$C N CH$_3$

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What is the meaning of scarcity? a. Rare b. Unlimited wants and limited resources c. Unlimited Resources d. Limited choice

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There are many applications of matrices you may see in the future. One of these is common in a mathematical discipline called cryptography, which is the science of encrypting and deciphering messages. A simple way to encrypt is to have the inverse of the encryption matrix, then you and I can communicate and others would be unable to decipher the message. We do not yet have the tools needed to send and decipher a message, but we can use what we have done this week to generate an inverse matrix that could be used to decipher a message with the same number of rows and columns of the same dimension of our encryption matrix, and which has 1s along the primary diagonal and 0s in all other cells. For a 2x2 matrix, the identity matrix would be: [1 0] [0 1] To find the identity matrix when you are given some matrix A: 1. Set up the augmented matrix [A|I] where I is the identity matrix 2. Use elementary row operations to convert the encryption matrix into the identity matrix 3. The end result will be [I|B] where B is the deciphering matrix. For this week's problem, find the deciphering matrix for the encryption matrix, A, below. You must correctly identify all row operations using the notations developed this week. [5 1] [3 1]

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$\frac{c^2}{k}F(\frac{\Delta T_r}{\Delta T_c})$ where $F$ is an unknown function. (b) Assume that for all turkeys $V = C l^3$ where $V$ is the volume of the turkey, and $C$ is a dimensionless constant. Two turkeys with masses $m_1$ and $m_2$ take times $t_1$ and $t_2$ to fully roast, respectively. Using your result from part (a), show that $\frac{t_2}{t_1} = (\frac{m_2}{m_1})^{2/3}$ assuming that $\Delta T_r$ and $\Delta T_c$ are the same for both turkeys. (c) When roasting turkeys, it is sometimes assumed that the cooking time is simply proportional to the mass of the turkey. For example, if it takes 4 hours to fully roast a 5 kg turkey, then it is assumed to take 8 hours to fully roast a 10 kg turkey. Comment on the wisdom of this assumption in view of your result in part (b).

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6. Si$_3$N$_4$ has a surface energy equal to 3 J/m$^2$, a Young's modulus of 350 GPa and an atomic spacing of 0.2 nm. Estimate the theoretical strength of this material. 7. The experimentally observed fracture stress of Si$_3$N$_4$ in tension is 550 MPa. Calculate the flaw size that would cause this failure stress, if the fracture toughness, K, of Si$_3$N$_4$ is 5 MPa m$^{1/2}$

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13. Use the selection sort to sort the numbers in the int array i a. Use calls to System. currentTimeMillis before and after the sort to determine the elapsed time: long start = System.currentTimeMillis(); // do sort long stop = System.currentTimeMillis(); System.currentTimeMillis returns the current time in milliseconds. Thus, to get elapsed time in seconds, divide the difference in the start and stop times by 1000.0. Then round the result to the nearest long value by calling Math.round: long elapsed = Math.round((stop - start)/1000.0); Determine the size of ia for which the elapsed time of the sort is about 100 seconds. Now perform the same sort using the static sort method in the Arrays class in the java.util package. Call this method with Arrays.sort(ia); What is the elapsed time for this sort? Is this sort significantly faster than the selection sort? 13b) Implement and test a bubble sort. To sort n numbers, make n - 1 passes. On each pass, compare every pair of adjacent numbers. If any pair is not in ascending order, switch the pair. On the first pass, start from the first element (compare the first with the second, the second with the third, and so on). On the second pass, again start from the first element but stop your compares one slot from the end of the array. In each successive pass, stop one slot before the stopping point of the previous pass. Use your bubble sort to sort 100, 23, 15, 23, 7, 23, 2, 311, 5, 8, and 3. Display the sorted numbers.

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3. A connecting rod has a mass or 4 kg. It oscillates 50 times in 1 min when suspended on a knife edge about the upper inner surface of the wrist pin bearing. Determine the mass moment of inertia of the rod about the centriod which is located 185 mm from the surface. What is the natural frequency $\omega_n$ of this rod?

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