Printable cartesian plane graph paperm

So, having found my way back to the wars after a long hiatus that has seen the fragmentation of my lance, the death of our war master and the birth of my children who wish to fight the clan scum along side Dad I have found myself in a somewhat unique'ish situation.
In the intervening decades I went and got myself trained as a 2d/3d draftsman and somehow acquired the skills and tools necessary to create sprawling environments.
The rub comes that we, my lance and I, were never into tabletop or miniatures, it was all hex graphing notebooks, tokens and "your imagination". And so, I am somewhat lacking in how do hexmaps "do".
So with a hex being 30m flat to flat, that yeilds ~780m² (technically 779.4229 but I'm willing to chalk it up to metrology error) per hex; the physics of a battlemech sharing a hex with infantry and mechanized infantry, armor and artillery etc makes sense: they are where the legs aren't but how many fit in a hex? Not like a breaching stack but how do we handle two friendly mechs transiting a hex, say the mouth of a canyon.
Next up, unlike our bubble verse timeline where we developed rectilinear architectural and grid based Cartesian mapping systems, I have to only assume that in the BT bubble, they developed a hexalinear system because why else would there be hexagonal natural features (unless of course the whole hexagonal water thing IS true?!?) and hexagonal building systems etc. I cannot see a system where 30m wide roads are the norm so do you all just develop a "square" urban/suburban/industrial space and lay a hex grid over it?
To tie this all together I have the capacity to do civil drafting in Autocad in 2d from a plan view, add elevation isolines and do some elevation extrusion to create actual terrain and/or create a simplified land form with a corresponding elevation profile, say a long run of valley flanked by hills and plains. Additionally, an urban system is simple enough to do on a NY grid, DC radian grid or even an old world grape bunch plan. Biome can likewise be shown via hatch patterns & colors and the whole thing could be displayed simply with iso lines for elevations on an E sheet.
Many jumps in the past I found that a number of coworkers were involved with the SCA and we did some work together which culminated in the preparation of a D&D hex map in plywood scaled to their miniatures and using model railroad trees etc. it was a mountain with valleys and some plains with forests all fitted to a folding ping-pong table. I'd love to do something like that again but I don't have free access to a cnc router and a growing pile of off fall anymore, I can schedule and pay for it but baby steps, gotta see how deep the lads wish to go first.

I`m trying to analyze pitch torque of aircraft. I ususally do a stability analysis via XFLR5 and then compare with Ansys. The lift and drag values are the same, when accounted for the fuselage. The shape of the graphs etc is consistent, but the torque values are way off. Like 1000% off. I made sure my coordinate systems for torque are OK. Both forces and torques are collected as force_x()@Default Domain Default. I ran mesh sensitivity studies and found that 1-1.5 mln nodes is enough for the values to be independent from mesh. I even tested the approach on an RC plane design I know is stable and flyable. XFLR5 says its stable, ansys says its not. What should i check? Meshing? viscid/inviscid analysis? What wall type must the aircraft surface be? slip or no slip? I`m assuming the surface is smooth. The fluid domain is about 5 times bigger than the aircraft in every direction. The problem manifests itself the same way with different geometries of aircraft. I will be glad for any help and hints.

some things you should definitely go over before the exam, feel free to add anything if i forgot to mention it, good luck on your exam guys!!
1) emf and internal resistance, learn how to calculate them from the graphs ( emf is the y-intercept) (internal resistance is -gradient)
2) the relationships between p.d. current and resistance. how temperature affects it
3) factors impacting resistance
4) compare and contrast between unpolarized light and plane polarized light.
5) learn the definitions of: emf, work function, transverse wave, longitudinal wave, current, refraction
6) be able to explain the shape of diode, and filament lamp
7) derive equations for conservation rules and ohms law
8) conditions needed for TIR to take place
9) huygens principle
10) d= distance between two adjacent lines
11) learn photoelectric effect
12) learn why the wave model can’t explain photoelectric effect
13) relationship between work function and maximum speed of electrons
14) ev to J (x1.6x10^-19)
15) hydrogen emission spectra
16) why only certain wavelengths of light emitted
17) nm to m (x10^-9)
18) mA to A (x10^-3)
19) light years (how many light years there are multiplied by 365x24x60x60x3.00x10⁸⁾
20) mm to m (x10^-3)
21) wavelength = 2/ nth harmonic x L
22) energy conservation
23) charge conservation

I have no clue how to do this and all videos online are not similar and my textbook only does stuff involving Cartesian planes so please help if you know how to do this.

When a tiny part in my Beseler c-6’s focal plane shutter broke I found myself without a way to use my Aero-Ektar. Much caffeine later, I designed this camera. Credit for the original shutter design goes to Jan on Printables - I scaled their model up 50% and made a few tweaks for this camera’s shutter, which does around 1/45th at it’s fastest setting. First test shots on instax film are promising (lomograflock) and will be shooting some fp4 soon.

With the Physics C exams coming up in 2 days, I thought I'd share some tips. Feel free to give me some tips in return :)
Calculator Stuff:

1. Store all the important constants on your calculator (G = 6.67E10-11, μ = 4πE-7, ε = 8.85E-12, electron mass = 9.11E-31, proton mass = 1.67E-27, k = 9E9, e = 1.6E-19). This is very important because it minimizes the chance of miscalculation and saves you a bit of time. Basically just type the value, then press the STO button, then press the alpha key and a button with the green letter you want.
2. Don't forget to switch your calculator to degree mode before the exam. The test is a day after AP calc, so a lot of people will probably be in radians. In some cases you'll need radians (sometimes it's important for SHM and electrostatics) though, so keep that in mind too.
3. When typing in exponents into your calculator, use the EE button (click on 2nd then the comma, then type the amount of times you want to multiply by 10). It's way easier than using the 10^x button and manually typing out the exponent and minimizes the chance of mistakes.
4. If you have a really big or small number that isn't automatically converted into scientific notation, instead of counting the digits, change the calculator mode to "SCI" and enter the answer again to get it in scientific notation. Don't forget to change back to normal when you're done.

General Strategies:

1. Pay attention to what the FRQ is asking you to do. If it asks you to "determine" something and especially if it asks you to justify your numerical answer, usually you'll get full credit for writing just the answer down, and it's possible the answer is 0. If it asks you to find, calculate, or derive something, show all of your steps. And obviously don't put a negative number down if it asks for the magnitude.
2. Pay attention to units for E&M (mechanics almost always has correct units given). If you write down the correct units for each numerical answer for an FRQ, sometimes you'll get a point just for that.
3. Write the "correct" version of a formula when showing work. For example, don't say that flux = EA or flux = BL, instead say that it equals the integral of E dA or B ds. Similarly, don't use force equivalences (or any other equivalences for that matter) without explicitly saying F = ma (i.e. don't say ma = -kx without writing F = ma).
4. Don't forget the negative signs (or do forget them if it asks for magnitude) for stuff like torque (for all clockwise torques), dU/dx, spring force, and potential difference. Sometimes the negative direction is up too for forces too depending on the context.
5. If an MCQ has a wall of text or a complex pictorial representation, just skip it. Time is unbelievably scarce on this exam, so use it wisely.
6. If you encounter a linearization (line of best fit) question (they appear on basically every recent exam year so you should definitely be prepared for it), write an equation in the form y = (m)x + b, and use this to analyze what would happen if one or more variables were changed (those questions pop up a lot with linearization problems). Make sure to use points on the line of best fit and not points given on the graph to calculate the slope, because if the points are far enough from the line

Annoying Equations to Derive that aren't on the equation sheet (you should know how to work backwards from most of these):
Mechanics
W = Δ K
W = -Δ U (for conservative forces)
W = Δ E (change in thermal energy, i.e. friction. Only applies to external work)
v = sqrt(GM/r) (derive from cons. of energy)
T = sqrt(4 π ²r³/GM) (derive from Kepler's Law & Newton's 2nd Law)
K = -0.5 * U (only for circular orbits, derive from subsitution)
E = 0.5 * U (only for circular orbits, derive from substitution)
U = U1 + U2 + ... (for gravitational potential energy)
E & M
U = U1 + U2 + ... (for a system of particles)
a = qE/m for a particle (derive from Newton's 2nd law)
E = 2kq/rl for an infinite line of charge (derive from Gauss's Law)
E = q/2Aε for an infinite plane of charge (derive from Gauss's Law)
E = q/Aε for parallel plates (derive from Gauss's Law)
Σ E = E1 + E2 + ...
I = I0e^-t/RC for RC circuits (derive with Kirchoff's Loop Law diff eq)
Q = Q0e^-t/RC for discharging RC circuits (derive with Kirchoff's Loop Law diff eq)
V = V0e^-t/RC for discharging RC circuits (derive with Kirchoff's Loop Law diff eq)
Q = Q0(1 - e^-t/RC) for charging RC circuits (derive with Kirchoff's Loop Law diff eq)
V = V0(1 - e^-t/RC) for charging RC circuits (derive with Kirchoff's Loop Law diff eq)
B = μI/2πr for a wire (derive with Ampere's Law)
B = μI/4r for a semicircular loop (derive with Biot-Savart Law)
r = mv/qB for radius of curvature of a particle moving through a B field (derive with Newton's 2nd Law)
F = μl(I1I2)/2πd for force between parallel wires (derive from magnetic force on a wire)
ε = vLB (induced voltage for a moving loop, derive with definition of voltage or Faraday)
L = μN²A/l (inductance of a solenoid, derive from definition of inductance)
E = vB for a moving loop (derive from Newton's 2nd Law)
E = 0.5r dB/dt for a solenoid (derive from Faraday)

I'm trying to recreate a plot like this (panel A), but with the colours on the surface of a sphere (similar to this). So the top and bottom (Z axis) of the sphere should be blue, the front and back (X axis) should be red, and the left and right (Y axis) should be green.
My idea is to use the XYZ coordinates of points on the surface of the sphere as RGB values, e.g. if the coordinate is 1,0,0 (the tip of the back of the sphere), then the RGB value of 1,0,0 = red.
However, when I try and plot this, the surface doesn't have the the desired RGB colours (see image).
What am I doing wrong?
Here's my code:

import plotly.graph_objects as go import numpy as np from matplotlib import cm # Create a grid of theta and phi values theta = np.linspace(0, 2 * np.pi, 100) phi = np.linspace(0, np.pi, 100) # Create the meshgrid theta, phi = np.meshgrid(theta, phi) # Define the radius of the sphere r = 1 # Convert spherical coordinates to Cartesian coordinates x = r * np.sin(phi) * np.cos(theta) y = r * np.sin(phi) * np.sin(theta) z = r * np.cos(phi) # Combine absolute values of X, Y, and Z to get final color color = np.stack([np.abs(x), np.abs(y), np.abs(z)], axis=1) # Create the plotly figure fig = go.Figure(data=[go.Surface(x=x, y=y, z=z, surfacecolor=color)]) # Update layout fig.update_layout(scene=dict(aspectmode="data")) # Show the interactive plot fig.show() 

Determine the projection of:
x^2 + y^2 − 4z^2 = 4
x + y = 2
in the xy-plane
I found the domain of z to be x^2+y^2>=4 but graphing it on desmos, it doesn't seem to make much sense.
Any help explaining it would be appreciated.

Determine the projection of:
x^2 + y^2 − 4z^2 = 4
x + y = 2
in the xy-plane
I found the domain of z to be x^2+y^2>=4 but graphing it on desmos, it doesn't seem to make much sense.
Any help explaining it would be appreciated.