A rosette strain gage is an electromechanical device that can measure relative surface elongations in three directions. Bonding such a device to the surface of a structure allows determination of elongational strains in particular directions. A schematic of one such gage is shown in the following figure, and the output of the device will provide data on the strains along the gage arms a, b, and c. During one application, it is found that e_a = 0.001, e_b = 0.002, and e_c = 0.004. Using the two-dimensional strain transformation relations, calculate the surface strain components e_x, e_y, and e_xy.

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y 60 b m m 60 mmm X a