1. After applying Principal Component Analysis (PCA) on five variables from the Breakfast Cereals dataset (calories, protein, fat, sodium, and fiber), the importance of components are summarized below:

	PC1	PC2	PC3	PC4	PC5
Standard deviation	84.0474	18.55527	2.37106	0.91753	0.80417
Proportion of Variance	0.9526	0.04643	0.00076	0.00011	0.00009
Cumulative Proportion	0.9526	0.99904	0.9998	0.99991	1

The rotation matrix is:

	PC1	PC2	PC3	PC4	PC5
calories	0.073	0.996	-0.032	0.027	0.021
protein	-0.001	0.002	-0.289	-0.821	0.493
fat	0.000	0.028	-0.091	-0.489	-0.867
sodium	0.997	-0.073	0.000	-0.002	-0.001
fiber	-0.002	-0.037	-0.952	0.295	-0.067

The mean of the five variables are listed below:

	Mean
calories	106.883
protein	2.545
fat	1.013
sodium	159.675
fiber	2.152

Given the following three Breakfast Cereals products, compute their scores of the first and the second principal components.

Cereal Product	calories	protein	fat	sodium	fiber	PC1	PC2
Froot_Loops	110	2	1	125	1
Wheaties_Honey_Gold	110	2	1	200	1
100%_Natural_Bran	120	3	5	15	2