Example: Increasing the tension in A string causes the speed of waves on the string to increase. Since the wavelengths of the standing waves remains constant, this results in a larger frequency of oscillations in the string, which we percieve as a higher pitch when the string vibrates the air.
Ignoring air resistance . . .
After the bomb is released, tangential (horizontal) acceleration is zero,, normal (vertical) acceleration is 9.8 m/s^2 down (gravity).
Answer:
A. False
B. False
C. True
D. True
E. True
F. True
Explanation:
A. The equation Ax=b is referred to as a matrix equation and not vector equation.
B. If the augmented matrix [ A b ] has a pivot position in every row then equation Ax=b may or may not be consistent. It is inconsistent if [A b] has a pivot in the last column b and it is consistent if the matrix A has a pivot in every row.
C. In the product of Ax also called the dot product the first entry is a sum of products. For example the the product of Ax where A has [a11 a12 a13] in the first entry of each column and the corresponding entries in x are [x1 x2 x3] then the first entry in the product is the sum of products i.e. a11x1 + a12x2 +a13x3
D. If the columns of mxn matrix A span R^m, this states that every possible vector b in R^m is a linear combination of the columns which makes the equation consistent. So the equation Ax=b has at least one solution for each b in R^m.
E. It is stated that a vector equation x1a1 + x2a2 + x3a3 + ... + xnan = b has the same solution set as that of the linear system with augmented matrix [a1 a2 ... an b]. So the solution set of linear system whose augmented matrix is [a1 a2 a3 b] is the same as solution set of Ax=b if A=[a1 a2 a3] and b can be produced by linear combination of a1 a2 a3 iff the solution of linear system corresponding to [a1 a2 a3 b] takes place.
F. It is true because lets say b is a vector in R^m which is not in the span of the columns. b cannot be obtained for some x which belongs to R^m as b = Ax. So Ax=b is inconsistent for some b in R^m and has no solution.
Depends on the weight of the bird.
1) Half a mile is about 800m.
2) 14000 lbs = about 6 tones, same like couple 4WD
3) Fuel consumption is about 20L per 100km or 0.2l each 1km or 0.16L within 800m
4) density of fuel is about 70% of density of water so .... weight of 1.6L of fuel burned would be about 1.6*0.7=1.1 kg
So if birds mass would be below 1 kg - the bridge will not collapse. But if it would be a pelican with the mass of 9kg - it would be a drama :)
Transverse( propagation perpendicular vibration)
Longitudinal ( propagation parallel vibration)
