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Section B. (2 marks each for parts a and band 2 marks for parte, totaling 4...
Question 4 (2+1+1+4+2 = 10 marks) a) Draw the chemical structure of 2,6-dibromo-3,4-dimethylphenol. (2 marks) b)...
Question 4 (2+1+1+4+2 = 10 marks) a) Draw the chemical structure of 2,6-dibromo-3,4-dimethylphenol. (2 marks) b) Will this molecule be a stronger or weaker acid than ethanol? (1 mark) c) How many unique signals would be observed in the mark) C NMR spectra of this molecule? (1 d) Using Huckel's rules, determine whether the following molecules are aromatic or not. How many pi electrons do each of these molecules contain? (4 marks) e) Draw the product of the following reaction....
16) Convert to a logarithmic equation: 20° = 400 (2 marks) 17) Convert to an exponential...
16) Convert to a logarithmic equation: 20° = 400 (2 marks) 17) Convert to an exponential equation: b=log, 243 (2 marks) 18) Find: log, 1 (2 marks) 19) Find the common logarithm, to four decimal places, using a calculator: log 0.2114 (1 mark) 20) The pH of a substance is 5.2. Find the hydrogen ion concentration in moles per litre (Use pH = -log[H]. Express the answer in scientific notation.) (5 marks) 21) Sixteen plus three times a number is...
Part B (Attempt four (4) questions only from this section, each question carries 150 Marks) QUESTION1...
Part B (Attempt four (4) questions only from this section, each question carries 150 Marks) QUESTION1 (A) specimen and the data is plotted in the below figure. performed on a A tensile test was 52 48 44 40 36 32 28 24 16 12 4- 1 3 4 5 6 7 9 Deformation, mm The specimen has an initial diameter of 10 mm and an initial gauge length of 50 mm. By using the data and plotted graph, determine the...
Extended Answer Section There are three questions in this section, each with a number of parts. Write your answers...
Extended Answer Section There are three questions in this section, each with a number of parts. Write your answers in the space provided below each part. If you need more space there are extra pages at the end of the examination paper. 1. (12 marks in total) (a) Let u and v be the vectors u 2i +j - 6k and v = 2i - k. Resolve u into a sum of two vectors, one parallel to v and the...
Report Date 01- 31- 20 Section Chem is 1. Write each number in scientific notation. 10cm...
Report Date 01- 31- 20 Section Chem is 1. Write each number in scientific notation. 10cm a the average height of adult 182.88 cm b. speed of light 186,282 m/s c. length of X rays 0.000 000 009 m d. one pound of water contains 3892000 L 2. Convert these numbers to decimal format. a. 1.36 x 10' g/cm b. 4.39 x 10-7 mm c. 45.4 x 10g d. 1.760 x 10'yd 3. Perform the following calculations then write your...
F GHANA served) TEF RO HC 3 -2 0 A2. Given the matrix below 5 marks) [5 marks (10 marks (b) Compute explicitly the eige...
F GHANA served) TEF RO HC 3 -2 0 A2. Given the matrix below 5 marks) [5 marks (10 marks (b) Compute explicitly the eigenvalues and determine the determinant, (c) Compute the corresponding eigenvectors of the matrix above (a) Show that the matrix is positive definite. 1 | so that the characteristic polynomial 5 marks 0 (d) Choose a, band c in the matrix B = | 0 Based on Cayley-Hamilton's theorem, every matrix fulfills its characteristic polynomial, using the...
5. Let (a) (2 marks) Find all eigenvalues of A (b) (4 marks) Find an orthonormal basis for each e...
5. Let (a) (2 marks) Find all eigenvalues of A (b) (4 marks) Find an orthonormal basis for each eigenspace of A (you may find an orthonormal basis by inspection or use the Gram-Schmidt algorithm on each eigenspace) (c) (2 marks) Deduce that A is orthogonally diagonalizable. Write down an orthogonal matrix P and a diagonal matrix D such that D P-AP. (d) (1 mark) Use the fact that P is an orthogonal matrix to find P-1 (e) (2 marks)...
need #2 Section #3: For Each of the following Metal-Semiconductor Junctions answer all parts A. Sketch...
need #2
Section #3: For Each of the following Metal-Semiconductor Junctions answer all parts A. Sketch the Band-Bending diagram at UV bias B. Identify the type of Junction and label the polarity of the space charge region. Assume OV bias. C. Sketch the Band-Bending diagram under Forward Bias D. Sketch the Band-Bending diagram under Reverse Bias 1. Metal: Aluminum (W = 4.25eV). Semiconductor: Silicon (NA = 1e15cm, No = 1e5cm) 2. Metal: Cadmium (W= 4.08eV). Semiconductor: GaN (NA = Ocm,...
Section B (50 marks) Answer any two questions from this section. All questions carry equal marks....
Section B (50 marks) Answer any two questions from this section. All questions carry equal marks. 1. (a) The density function of X is given by $(x) = { a + bx?, OSX31 0, otherwise If E[X] = , find i. the cumulative density function, F(X). [5 mark ii. P(x < [3 mark (b) Given the observations Ii, i = 1, 2 and their corresponding weight, W;, i = 1, show that the weighted average Xw = 221 + (1...
Problem 4 (12 points, 2 for each part) In each of the following parts, as- sume...
Problem 4 (12 points, 2 for each part) In each of the following parts, as- sume that the matrices A, B, C have sizes that make the sums, differences, and products in that part well-defined. Say whether the statement is always true (i.e., true for all matrices of appropriate sizes), sometimes but not al- ways true, or always false. (You may abbreviate answers as T, S, and F, respectively, but make sure your handwriting is unambiguous.) (a) AB = BA...
Question 4 (2+1+1+4+2 = 10 marks) a) Draw the chemical structure of 2,6-dibromo-3,4-dimethylphenol. (2 marks) b) Will this molecule be a stronger or weaker acid than ethanol? (1 mark) c) How many unique signals would be observed in the mark) C NMR spectra of this molecule? (1 d) Using Huckel's rules, determine whether the following molecules are aromatic or not. How many pi electrons do each of these molecules contain? (4 marks) e) Draw the product of the following reaction....
16) Convert to a logarithmic equation: 20° = 400 (2 marks) 17) Convert to an exponential equation: b=log, 243 (2 marks) 18) Find: log, 1 (2 marks) 19) Find the common logarithm, to four decimal places, using a calculator: log 0.2114 (1 mark) 20) The pH of a substance is 5.2. Find the hydrogen ion concentration in moles per litre (Use pH = -log[H]. Express the answer in scientific notation.) (5 marks) 21) Sixteen plus three times a number is...
Part B (Attempt four (4) questions only from this section, each question carries 150 Marks) QUESTION1 (A) specimen and the data is plotted in the below figure. performed on a A tensile test was 52 48 44 40 36 32 28 24 16 12 4- 1 3 4 5 6 7 9 Deformation, mm The specimen has an initial diameter of 10 mm and an initial gauge length of 50 mm. By using the data and plotted graph, determine the...
Extended Answer Section There are three questions in this section, each with a number of parts. Write your answers in the space provided below each part. If you need more space there are extra pages at the end of the examination paper. 1. (12 marks in total) (a) Let u and v be the vectors u 2i +j - 6k and v = 2i - k. Resolve u into a sum of two vectors, one parallel to v and the...
Report Date 01- 31- 20 Section Chem is 1. Write each number in scientific notation. 10cm a the average height of adult 182.88 cm b. speed of light 186,282 m/s c. length of X rays 0.000 000 009 m d. one pound of water contains 3892000 L 2. Convert these numbers to decimal format. a. 1.36 x 10' g/cm b. 4.39 x 10-7 mm c. 45.4 x 10g d. 1.760 x 10'yd 3. Perform the following calculations then write your...
F GHANA served) TEF RO HC 3 -2 0 A2. Given the matrix below 5 marks) [5 marks (10 marks (b) Compute explicitly the eigenvalues and determine the determinant, (c) Compute the corresponding eigenvectors of the matrix above (a) Show that the matrix is positive definite. 1 | so that the characteristic polynomial 5 marks 0 (d) Choose a, band c in the matrix B = | 0 Based on Cayley-Hamilton's theorem, every matrix fulfills its characteristic polynomial, using the...
5. Let (a) (2 marks) Find all eigenvalues of A (b) (4 marks) Find an orthonormal basis for each eigenspace of A (you may find an orthonormal basis by inspection or use the Gram-Schmidt algorithm on each eigenspace) (c) (2 marks) Deduce that A is orthogonally diagonalizable. Write down an orthogonal matrix P and a diagonal matrix D such that D P-AP. (d) (1 mark) Use the fact that P is an orthogonal matrix to find P-1 (e) (2 marks)...
need #2
Section #3: For Each of the following Metal-Semiconductor Junctions answer all parts A. Sketch the Band-Bending diagram at UV bias B. Identify the type of Junction and label the polarity of the space charge region. Assume OV bias. C. Sketch the Band-Bending diagram under Forward Bias D. Sketch the Band-Bending diagram under Reverse Bias 1. Metal: Aluminum (W = 4.25eV). Semiconductor: Silicon (NA = 1e15cm, No = 1e5cm) 2. Metal: Cadmium (W= 4.08eV). Semiconductor: GaN (NA = Ocm,...
Section B (50 marks) Answer any two questions from this section. All questions carry equal marks. 1. (a) The density function of X is given by $(x) = { a + bx?, OSX31 0, otherwise If E[X] = , find i. the cumulative density function, F(X). [5 mark ii. P(x < [3 mark (b) Given the observations Ii, i = 1, 2 and their corresponding weight, W;, i = 1, show that the weighted average Xw = 221 + (1...
Problem 4 (12 points, 2 for each part) In each of the following parts, as- sume that the matrices A, B, C have sizes that make the sums, differences, and products in that part well-defined. Say whether the statement is always true (i.e., true for all matrices of appropriate sizes), sometimes but not al- ways true, or always false. (You may abbreviate answers as T, S, and F, respectively, but make sure your handwriting is unambiguous.) (a) AB = BA...
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