For the crystal lattice and atomic basis vectors for graphene discussed in class: (A) Calculate the x and y positions of the A and B atoms at position R=(na1+ma2) for arbitrary n,m. You will use this for the next problem set. (B) Calculate the area per unit cell in graphene, and the number of atoms per unit area (in #/cm2 ). Use this result to calculate the density of a single of layer graphene in units of kg/m2. (C) Look up the value of the interlayer spacing in graphite and use this value to calculate the density of graphite. Check this against the standard density of graphite. (D) [grad students only] Repeat (A-C) above for MoS2. For (A), give the x,y,z positions of the single Mo atom and two S atoms. You can find lattice constants for MoS2 here: https://materialsproject.org/materials/mp-2815