The Ghost of Hamlet's father is, understandably, the source of most of the references to anger in the opening act of Hamlet. The first such quote appears in an early exchange between Marcellus and Horatio as they describe their recent sighting of the Ghost:

So frowned he once when, in an angry parle,
He smote the sledded Polacks on the ice. (1.1.73–74)

The next quote is taken from Hamlet's soliloquy following his first exchange with Claudius and Gertrude in which he discusses the disgust and anger he feels toward his mother for marrying so quickly after his father's death:

Let me not think on't; frailty, thy name is woman! (1.2.150)

The third reference to anger also occurs in 1.2, as Hamlet learns from Horatio and Marcellus that they've recently spied the Ghost of his late father. In response to Hamlet's question about whether the Ghost look "frowningly," Horatio replies:

A countenance more in sorrow than in anger. (1.2.247)

The remaining quotes which bear some relation to anger are taken from the 1.5, the scene in which the Ghost reveals to Hamlet the manner of his death. In the midst of his tale, the Ghost lashes out at Claudius, and begs for revenge:

O horrible, O horrible, most horrible!
If thou hast nature in thee, bear it not. (1.5.87–88)

And after hearing the Ghost's full account, Hamlet explodes in anger:

O all you host of heaven! O earth! what else?
And shall I couple hell? O, fie! Hold, hold, my heart;
And you my sinews, grow not instant old,
But bear me stiffly up. (1.5.99–102)