The surface tension of a fluid depends upon the viscosity μ, bulk modulus EV, gravity g, pressure p, velocity v, density Ƿ, and a characteristic length L. determine the dimensionless groupings. USE MLT and V, L, Ƿ as repeating variables. A your Pi terms among the common dimensionless groups in Fluid Mechanics?

Three jars each have volume V and height h, but they have different shapes as shown in (Figure 1) . Water is to be added to each jar and the pressure is to be measured right at the bottom of each jar.

Figure 1

Part A

Rank the jars in order of decreasing pressure if the volume of water is V.

Rank from largest to smallest. To rank items as equivalent, overlap them.

P_a, P_{c ,} P_b

or correct ranking cannot be determined.

Part B

Rank the jars in order of decreasing pressure if the volume of water is V/2.

Rank from largest to smallest. To rank items as equivalent, overlap them.

P_{b ,} P_{a ,} P_c

or correct ranking cannot be determined

Why is Budgeting and Tax Planning shown as the first component of a financial plan? Budgeting and tax planning form the foundation for other components of the financial plan. Retirement and estate planning only apply to those in later life stages. Almost every financial decision has a tax impact that must be taken into consideration. Lack of budgetary control will prevent the ability to save, acquire assets and pay expenses. Investment cannot occur without the ability to save. A primary financial objective should be to minimize one’s tax bill. I, II, III and IV I, III, IV and V II, IV, V and VI I, II, V and VI

The question is to use Matlab to find the clamped cubic spline v(x) that interpolates a function f(x) that satisfies: f(0)=0, f(1)=0.5, f(2)=2, f(3)=1.5, f'(0)=0.2, f'(3)=-1 and then plot v(x).

This is my code so far:

x = [0 1 2 3];

y = [0 0.5 2 1.5];

cs = spline(x,[0 y 0]);

xx = linspace(0,3,101);

figure()

plot(x,y,'o',xx,ppval(cs,xx),'-');

IS THIS RIGHT? HOW CAN I GET MATLAB TO GIVE ME THE EQUATION OF v(x)?

Let p be an odd prime (i.e., any prime other than 2). Form two vector spaces V₁, V₂ over F_p (prime field of order p) with bases corresponding to the edges and faces of an icosahedron (so that V₁ has dimension 30 and V2 has dimension 20). Let T : V₁ → V₂ be the linear transformation defined as follows: given a vector v ∈ V₁, T(v) is the vector in V₂ whose component corresponding to a given face is the sum of the components of v corresponding to the edges around that face. Prove that T is surjective. (Hint: one option is to look closely at the five edges emanating from a single vertex.)

A fixed number of moles of an ideal gas are kept in a container of volume V and an absolute temperature T.
If T doubles while V is held constant, the new net internal energy of the gas will be ________ times the original internal energy of the gas.

If T and V are both doubled, the new r.m.s. velocity of the molecules in the gas will be _________ times the original r.m.s. molecular velocity.

Determine the amounts of the solutes necessarry to prepare the indicated solutions.

A) 4L Dialysis Buffer (25mM HEPES, 0.01% (v/v) Triton X-100, 300mM NaCl, 2.5M Urea)

B) 250mL 25x MES running buffer (1x= 50mM MES, 50mM Tris, 0.1% (w/v) SDS, 1mM EDTA)

C) 1:15,000 SYBR Green (25mg/mL0 in 80mL 0.8% agarose

D) What is the final micromolar concentration of SYBR Green in the agarose solution in Part C?

Formula Masses

Tris: 121.14

NaCl: 58.44

HEPES: 238.3

Urea: 60.06

MES: 195.24

EDTA:292.24

SYBR Green: 509.73

Which of the following are characteristics of

biological membranes?

(i) Membranes are fluid structures.

(ii) The sugar residues of membrane are always located on the external surface of plasma membranes.

(iii) The outer and inner surfaces of all known biological membranes have different components and different enzymatic activities, i.e., membranes are asymmetric.

(iv) Membrane fluidity is controlled by fatty acid composition and protein distribution.

(v) Membrane proteins and phospholipids can readily rotate within the membrane, from the inside to the outside surface.

Ball 1: m=1.8g, r=2cm & Ball 2: m=2.2g, r=2cm, Cylinder: V=24oz, m=17.2g

1) Find volume (V=4/3(pie)(r)^3) & density (p=m/V) for both balls

2) Find density of the cylinder

3) Draw free body diagrams of both balls on water (The upward force of the water on the ball is called the buoyant force)

4) Determine the net force on each ball. Show your work or explain your reasoning.

5) Determine the magnitude of the buoyant force on each ball, if possible. If not possible, explain why. Show your work.