This question is about Principal Components Analysis (PCA)and Exploratory Factor Analysis (EFA) by R programming.

(a) If we want to evaluate following performance of several students based on the score of 5 lessons, please use Principal Components Analysis (PCA) to generate the evaluation method (with R prommaing codes). And please list out the ranking of the students based on this evaluation method.

(b) Can we apply Exploratory Factor Analysis (EFA) in aforementioned data? Please present the result and the conclusion (with R prommaing codes). What's the similarities and difference between these two methods? Why should we do the rotation in EFA but not in PCA?

_{* Below is internal data.}

	History (X1)	Chinese (X2)	English (X3)	Physics (X4)	Math (X5)
Student 1	99	94	93	100	100
Student 2	99	88	96	99	97
Student 3	100	98	81	96	100
Student 4	93	88	88	99	96
Student 5	100	91	72	96	78
Student 6	90	78	82	75	97
Student 7	75	73	88	97	89
Student 8	93	84	83	68	88
Student 9	87	73	60	76	84
Student 10	95	82	90	62	39
Student 11	76	72	43	67	78
Student 12	85	75	50	34	37